I've looked around a bit to try and find a starting date, but it doesn't seem like they've announced it yet.
The preseason schedule starts on Tuesday, October 4th. And if I remember right, there's usually about two weeks of practice/training camp before the actual games start.
So that'd put training camp starting around September 19-20, which is only about two and a half to three weeks away!
I'm pretty pumped for this season, and the last several months have just been dragging by. Hopefully there's only a couple of more weeks before we get Celtics basketball back in our lives!