As long as your artificial grass was properly installed and supported then the trampoline should do no damage to the artificial grass.
Although the trampoline may leave an imprint in the artificial grass but usually it can be smoothed out again.
You could also get an in ground trampoline where most of the trampoline sits in the ground and also it's safer to have the trampoline inside the ground at ground level to prevent falls as well.
Then just install the artificial grass around the trampoline.