Best time of year to cut down tree in terms of recovery of yard

Live Northwest of Atlanta in a neighborhood that essentially every yard has a tree in the front. Issue is the trees roots are destroying everyones yard. Ive been told when they originally planted the tree they did the wrong type no idea if thats true or not but anyway. Trees roots are very much on surface and has killed all grass around it and a good portion of people in neighborhood are getting them cut down, stumps grinded, either putting nice flower beds in, or a new tree or just going straight grass.

What time of year is best to start this process to get grass coming back and do that whole process? Or does it really not matter?