It is a Live Oak, and the younger ones will lose their leaves the first few winter seasons, because it is a semi-evergreen, and not a true evergreen. As it matures, it will begin to lose leaves gradually, and replace them gradually, so that the fact it is doing so, will not be obvious, and it will appear evergreen.

That is normal for these.

Well I hope you're right. Unfortunately, I still think the tree is in distress as all of my neighbors' trees which were also transplanted by the HOA managed to keep most of their leaves over the winter. And I am worried that the new leaves are not appearing on the outer parts of the branches, which as I said are clearly dead. They break off easily and have no green core. Also, I have a live oak and it doesn't have the same shape leaf and doesn't produce acorns, but perhaps they are different types of live oaks.

The tree in question could be a Monterrey Oak. They have a larger and more lobed leaf than a Live Oak. They vary greatly in how "evergreen" they are also. I've noticed groupings of them where one will go bare and another will keep all its leaves.

I wouldn't give up just yet. Wait a few weeks and see what it does.

Make sure it's not planted too deep. Root flares should be exposed. For that size of tree, you'd be better off with 5 feet wide of compost and mulch to get it established quickly. Oaks take forever to establish if grass is allowed to grow up to the trunk.