Pruning is unlikely to help it thicken up. Pruning will encourage new growth, but that would be from the branch tips, rather than filling in the foliage along the branches. Which is what I assume you mean by thickening up :-))

If the tree was planted too deeply, that is why it is still struggling and there is nothing you can do at this point to hasten the recovery. Length of recovery from that sort of stress is measured in tree time rather than people time and the tree will take as along as it needs.

That you are already noticing some improvement is a good thing. Just make sure it receives the water it needs and let it be. And you might want to take some time to research how to train and prune young shade trees. This is an excellent website for that info with detailed drawings - you want to focus on the instructions for trees with a decurrent growth habit, which all maples have.

Thank so you so much, great advice! I do have one more question...on the branches where no leaves are growing, should I prune them off or might they grow leaves eventually?

Unless you can tell whether or not the branch is dead, I would wait till next year. As stated earlier it takes a while to recover from stress. If however the branch is dead you can remove them now.