Shakespeare co-founded the Lord Chamberlain's Men in 1594.
Shakespeare was a founding member of the Lord Chamberlain's Men in 1594, not 1596.
the theatre William Shakespeare built. The theatre William Shakespeare built in 1599.
He didn't. He was with the King's Men when he retired in 1613.
Shakespeare helped form the Lord Chamberlain's Men in 1594. The occupied the Theatre and the Curtain playhouses until 1599 when they dismantled the Theatre and rebuilt it in another location, changing the name to the Globe.
If you mean William Shakespeare then the theatre was called the Globe.
None. This was fifty years before he was born. Nor did he ever "join a theatre". A theatre is a building you put on plays in--you cannot join it any more than you can join a bridge or a warehouse. What Shakespeare joined was an acting company, called the Lord Chamberlain's Men, and he did it when the company formed in 1594 (he was a charter member), eighty years after the date you propose.
He acted in it.
William Shakespeare
There is speculation that Shakespeare acted for Pembroke's Men or Strange's Men, but there is not hard evidence of it. In 1594 he helped found the Lord Chamberlain's Men.
The Chamberlain's Men
globe theatre
the globe theatre