When was Islam founded?

Islam is an Arabic word that means submission to God (Allah in Arabic). Accordingly, Islam (or submission to God) is the principle on which is based all God creations of the universe and before the universe. This brings the date of founding Islam, in its broad sense, to the same date of universe creation. In this case, it would depend on when you believe this to be: 13.7 billion years ago is the mainstream accepted figure

However, if the question asks about Islam faith then its date is the date of mankind creation. All people were created on the principle of submission to God (Islam) and given the choice to have faith and submission to God (Islam) or to deviate from Islam and worship idols or partners to God. Accordingly all prophets; including Noah, Abraham , Moses, Jesus, and Muhammad (Peace be upon them) are sent by God to reorient people to right path to God by calling them to Islam (submission to God).

Islam per God revelation of Torah to prophet Moses is called Judaism. Islam per God revelation of the Bible to prophet Jesus is called Christianity. Islam per God revelation of Quran to Prophet Muhammad is called the very name Islam.

Islam religion per God revelation of Quran to prophet Muhammad was founded by the start of Quran revelation by God to prophet Muhammad through the Angel Gabriel (Jibril) in Mecca (currently in the Kingdom of Saudi Arabia) in year 610 AD. Quran revelation continued also when the prophet (peace be upon him) migrated to Medina (also in the Kingdom of Saudi Arabia) until prophet death in year 632 AD.
Islam started in 610 AD by Ubu'l Kassim, who then started going by the name "Muhammad"

For many Muslims the term "Islam" has two meanings: the Divine Religion of Submission to God's Will (often called Islam with a small "i") and the Institutionalized Belief as Found in Qur'an and Revealed by Mohammed's Prophecy (often called Islam with a capital "I").

islam with a small "i" is a concept that comes out of Islam with a capital "I" and projects the Established Religion of Islam back into the period before would have identified as Muslim. The purpose of said belief, in a functional sense, is to gird Islam in the history afforded by the Judeo-Christian prophetic lineage and ensure its authenticity. islam also affords the believer in Islam a continuity of tradition which Mohammed only continued and corrected as opposed to having the religion of Islam be an affront or disagreement with other divinely-inspired religions. Since islam is derivative of Islam, it does not actually exist prior to Islam.

Islam, as an Established Religion, was organized and directed by Mohammed, who was born in 570 C.E. at Mecca, in Saudi Arabia. According to Islam, he received revelations from God in Mecca in from the year 610-632 C.E. He was supported by several family members like his uncle Ali Ibn Talib and his first wife Khadija to pursue these prophecies. He converted other members to his nascent religion before being expelled from Mecca to Yethrib (now known as Medina) in 622 C.E. When Mohammed became the Chief Hakam or Judge/Administrator of Yethrib, he received many new revelations and began to ask members of his community to memorize these revelations (along with prior ones). These memorizers (in Arabic Hafeths) would eventually be responsible for the creation of one unified Qur'an. By Mohammed's death, he had conquered all of Arabia and converted most of Arabia to his new faith, establishing the grounds for an Islamic Caliphate, which succeeded him.