He was in London by that time, and had written at least one play, because that is when Robert Greene made snarky remarks about him in his pamphlet A Groatsworth of Wit.
In London
1592-93
What theatre are you thinking of as "shakespeare's theatre"? Because Shakespeare did not own even a part of any theatre in 1592. Nor did he own even a part of any theatrical company. In fact he may not have even been a permanent member of any theatrical company at that time. There was nothing you could call "shakespeare's theatre" in 1592.
Between 1585 and 1592
William Shakespeare died in England in 1592. He was one of the most influential story tellers of all time.
People started noticing Shakespeare's work in about 1592 or so.
1592, by Robert Greene.
The Comedy of Errors
the plague
The Lost Years 1585-1592.
Sometime between 1585 and 1592.
1592 to the present, approximately, not including the period 1642-1660 when theatre was outlawed in England. The date 1592 is somewhat conjectural but we do know that someone in that year had seen a Shakespeare play performed.
The best one can say about when Shakespeare began his profession is that he had established himself before 1592.