Yes, because when Jesus died for our sins, the people who believed it became the first Christians. His disciples then went and spread the word. Christianity is named after Jesus and is based on His life and teachings but particularly on His death and resurrection.
According to Matthew 16:18, Jesus said to Peter, "You, Peter, are the rock upon which I will build my church." However, scholars widely question the authenticity of this alleged quotation; and many scholars (even some who don't question its authenticity) question the meaning of this statement, since the Greek term, "ekklesia," which was used there for "church," signified, in that time, any sort of an assembly, even a political one; and a Jewish assembly (or - as it was then called - "sunagoge") was also a type of "ekklesia." Did Jesus start a Jewish sect? Christianity isn't that. So, this statement, even if it was authentic, doesn't answer the question: Who started Christianity - and when, and where, and why?
The only other Scriptural candidate for Jesus having authorized Christianity is Matthew 28:18-20, in which the resurrected Jesus is quoted as ordering his followers, "Go throughout the world to make all peoples my disciples by baptizing them in the name of [the Trinity] the Father, the Son, and the Holy Ghost." However, this statement contradicts Matthew 5:17-20, which quotes Jesus as saying "Do not think I have come to do away with the Law of Moses, ... for it will be eternally binding," and the first three of the Ten Commandments permanently ban any such thing as the Trinity, and clearly demand worshiping only the Father, never to include any second object. Even more emphatically, the Third of the Ten Commandments says "Do not take the name of God in vain," and so this alleged baptismal order was clearly in violation. Furthermore, the early Christian church didn't consider this alleged statement from Christ to be binding, and as late as the 16th Century this order was widely understood as having been directed only at Jesus' disciples in his own time, not at future generations, and the obligation was thought to have been fulfilled by them. In any case, the statement doesn't assert that a person who fails to comply with it will be viewed less favorably by God, or denied salvation. Moreover, only relatively recently did the statement come to be called "The Great Commission," and considered as the start of Christianity. This change of belief occurred at the time critical scholarship on the Bible first emerged, The Enlightenment. It's not how Christianity had seen itself during the religion's first 1,600 years.
And if Jesus didn't create Christianity, if a different person created it, then would Jesus have approved of what that individual was doing? Might Christianity even have been created by an enemy of Jesus? Not only might this have happened; it did happen. And the most thorough documentation of it occurs in the New Testament itself, as we shall see.
Before it is possible to know whether Jesus (or anyone else) started Christianity, we must first have a satisfactory definition of "Christianity." Paul essentially defined "Christianity" (without even using the term) when he said in Galatians 2:16 "God approves only people who possess Christ-faith, never people who obey God's commandments." That doctrine is Christianity (salvation via Christ-faith), and it's replacing Judaism (salvation via obeying God's laws). And yet Matthew 5:17-18 quotes Jesus himself as having said, "Do not think that I have come to do away with the Law of Moses. ... As long as heaven and earth shall last, not the least point nor the smallest detail of the Law will be done away with." Jesus was teaching Judaism, but Paul - who admitted that he had never even met the living Jesus - said in Galatians 2:16-21 that the death and resurrection of Jesus meant that obeying God's commandments was no longer the way to please God.
After having applied modern courtroom analytical methods to investigate the evidence concerning the start of Christianity, I have identified the exact occasion at which Christianity (this doctrine: salvation via Christ-faith) actually started. Never before have these modern legal/forensic analytical methods been applied to this evidence; and these findings, reported in my new book (in press), The Event that Created Christianity, are that Paul knew he was violating Jesus' will when alleging, in Galatians 2:16, Romans 3:28, and elsewhere, that God now demanded faith in Christ, instead of obedience to God's laws.
I have found that in the year 49 or 50, Paul culminated a 14-year conflict he had had with Jesus' brother James, by perpetrating a coup d'etat against him and overthrowing him as the leader of the Jewish sect that Jesus had established 20 years earlier. I find that, according to Paul's own reluctantly made admission in Galatians (especially Galatians 2:12), Jesus had appointed James, not Peter, as Jesus' successor to lead Jesus' followers, and that the central conflict between Paul and James concerned Judaism's signature commandment, Genesis 17:14, at which God was alleged to have said to Abraham "No uncircumcised man will be one of my people." In the broader passage there, Genesis 17:9-19, God had offered to Abraham the Jewish covenant or agreement to sign, and said that it would be everlasting or eternal, and that the way it was to be signed was by circumcision. Every one of God's men must be circumcised, and would have any male child circumcised on his 8th day. Abraham complied, and thus Judaism - obedience to God's commandments or laws - started, according to the account in Jewish Scripture (which Jesus' followers accepted as reporting history, not merely as a myth).
Paul, however, had been bringing Gentile men into Jesus' sect for 17 years withoutrequiring them to be circumcised. According to Paul's account in Galatians, he first met James in the third year of his ministry, and his practice of accepting into the sect uncircumcised men was accepted both by James, and by Peter, Peter being at that time the chief person evangelizing to Gentiles. However, by the time of the 17th year of Paul's ministry, Paul had brought in such a large number of uncircumcised men, so that James called Paul back to Jerusalem to defend his practice. According to Galatians 2:10, the decision reached there was for Paul to continue what he was doing, so long as Paul continued raising funds to support the poor in Jerusalem - Jesus' disciples and their followers.
It's important to place these events in the broader context of the war that then was raging between Rome and the Jews, which was described in Josephus' works. Jews were at that time a conquered people, who had lost their independent Israel, and who were being ruled by kings appointed by Rome: the Herodian family were being imposed as their rulers. Jesus claimed to be the authentic king of the Jews, and this claim was sedition against Rome. It also threatened Roman Law, because Jesus was teaching that the Law came from God, not merely from Rome's Emperor or Caesar. This is why Rome had Jesus crucified, as a warning to any other Jew who might be so bold as to challenge Rome's authority to make all the laws and to appoint the kings. According to Josephus (Antiquities18:2:2), Rome also appointed the chief priest, in Jerusalem, Caiaphas. This is the actual reason why Caiaphas seized Jesus and handed him over to Rome's appointed Governor, Pontius Pilate, for trial on the charge of sedition against Rome. Caiphas thus was hired by Pilate, and did his bidding. Moreover, Jesus' followers were considered suspect, because they were followers of this man who had been convicted and executed for sedition by Rome. This historical background is essential to understand, in order to understand why Jesus' remaining followers, in Jerusalem, were politically vulnerable, and were very poor.
With this as background then: immediately after the council in Jerusalem, in the 17th year of Paul's ministry, James in Jerusalem sent Peter to Paul in Antioch (current-day Antakya Turkey) to tell Paul the bad news that James had changed his mind and would require, after all, that Paul's men be circumcised, in accord with this "eternal" and "everlasting" commandment (see Genesis 17:13&19). Paul in Antioch refused to comply, and announced Christianity, the doctrine he stated in Galatians2:16-21.
Here is why he refused: During the First Century, when there was no such thing as anesthesia, and also when neither antibiotics nor antiseptics existed, any operation, even a circumcision, was both a frightful terror and a threat of death (from infections). To impose this medical operation upon a male baby on its 8th day, as Jews routinely did in accord with Genesis 17:11, was very different from demanding that full-grown Gentile men subject themselves to this terror and possible death. That's the reason why James had, for 17 years, notdemanded that Gentile members be circumcised. But now, according to both Acts and Galatians, there were so many uncircumcised men who were calling themselves followers of Jesus, so that, in Acts 21:21, and elsewhere, Jews were rioting against Paul demanding him to have his men circumcised. According to Acts 15:1, the council in Jerusalem had been called by James precisely to consider this highly contentious circumcision-issue: Genesis 17:14.
Galatians 2:12 indicates that James changed his mind soon after the council and sent Peter to tell Paul to have his men circumcised, after all; and sent a follow-up team to arrive that evening to check up on whether Peter did his job. Peter was reluctant to do it. James had selected Peter for this mission because Peter had been Paul's teacher 14 years earlier, and did as Paul did now: accepted uncircumcised men into the sect. (See, for example, Acts 11:2.) James chose Peter to deliver to Paul the bad news because James knew that Paul knew that, if even Peter now accepted the necessity of imposing Genesis 17:14, Paul would have no continuing support at all from Jerusalem unless Paul imposed circumcision upon his men.
Galatians 2:11-21 presents Paul publicly having stood against his own teacher, Peter, and against the other representatives sent by James, and having announced (Galatians2:16) that God no longer required obedience to God's laws, and that from now on, mere Christ-faith is all that God requires in order to send a person to heaven instead of to hell after death. The event recounted in Galatians2:11-21 occurred in the year 49 or 50, in Antioch. This was the first time that Christianity (the doctrine announced by Paul in 2:16-21) had been announced by anyone, and so it shocked and dismayed both Peter and the other representatives from James.
When Paul called James' bluff on this occasion, and refused to comply, James was actually trapped: James' small and vulnerable group in Jerusalem needed the contributions and the other support to continue coming from Paul's far larger number of far-better-off followers throughout the Roman Empire. Thus, James mutely folded his cards; and, from that moment onward, Paul tacitly took over effective control of what originally had been the Jewish sect that Jesus had started and that James had inherited.
This event in the year 49 or 50, the first-ever occasion on which Christianity (the doctrine that Paul announced in Galatians 2:16-21) was announced, constituted Paul's coup d'etat against James, and the break with Judaism, the start of Christianity. Paul did it in order to save his career from collapse, to avoid having almost all of the men whom he had converted to Judaism leave him. After that occasion, Paul wrote the letters by which he is known, and he wrote these letters in such a way that he intentionally glossed over the question as to whether they still were Jews.
The authors of each of the four canonical Gospel accounts of "Jesus" (Matthew, Mark, Luke, and John) were actually followers of Paul, and not at all followers of Jesus/James. They wrote the actions and the words of "Jesus" to support Paul's agenda, including the Trinity, and the minimization of James. (Paul introduced the Trinity because he needed the Holy Ghost, Jesus's ghost, since Paul's sole authorization to preach for "Jesus" came from that ghost.) In turn, the later followers of Paul, during subsequent generations, assembled the New Testament, and wrote James out of the "historical" picture altogether. Peter was retroactively identified, by Paul's followers, to have been the leader whom Jesus had appointed; and the reason for this is that Peter had been Paul's teacher, and that the emerging Roman Catholic Church needed someone to serve as the "historical" link back to Jesus, since Paul himself had never met Jesus.
So, the answer to the question "Did Jesus start Christianity?" is that Christianity was instead started by Paul, in order to salvage his career as a missionary for the Jewish sect that Jesus had started. Paul, in the 17th year of his career was faced with choosing between retaining his members or else repelling them by demanding them to go under the knife in an era which lacked anesthesia, antibiotics and antiseptics. He chose to retain his members, even though he knew that by his abandonment of the Jewish covenant he was teaching the opposite of what Jesus had taught. The authors of the four Gospels were Paul's followers, who manufactured a "Jesus" that embodied Paul's agenda, not the agenda of Jesus.