They will grow without mulch but you will be dealing with weeds and potentially root rot. The mulch keeps temperatures down on the roots, feeds soil, holds moisture, and inhibits root rot.
That said, I have seen plenty of 20 or 30ft tall trees doing just fine planted right in a lawn with zero mulch.
If you do apply mulch you will want to put 10 - 15 cm thick 2 meters in diameter circle around the tree. And do that until the tree is a few years old and they can then self mulch. When you trim and shape the tree, chop that up and leave it on the root zone.