Installing artificial grass around a big tree can be done and also very common. It will require some techniques and good preparations:
You need to make sure to remove the shallow roots and the roots sticking out of the ground in order to have a smooth sub base to lay your turf.
Normally people need to leave an either round or square cutout around the tree for both design and water reasons.
Please let us know if you have any further questions by email or this online form: https://megagrass.com/pages/free-estimates