When should cross country flights occur in flight training
There is no prescribed threshold to cross that indicates when XC training should start.

I generally wait until after a student's first solo to start talking about cross country work.  The first solo is a massive psychological barrier and once the student realizes that they really can fly a plane by themselves, it gives them confidence to learn new stuff.

That said, you are at a 141 school.  They need to follow their approved training schedule.