I don't know anything about that species of oak, but I do have a live oak in my yard that I planted ~20 years ago, then shortly after that moved away (but kept the house) after retiring from the navy I returned and that live oak, which was only about 2 ft when I left is now ~50 ft. Never really did anything for that tree and it grew pretty well. Oaks are hardy trees and fast growers.
However, if I had to do it all over, I'd mulch a large area for it. That's what I've done since returning home and the foliage does seem much healthier. I don't just muclh a small circle, I've mulched a very large area, because the grass wasn't growing too well any way and I think it looks better with a large mulched area and healthy green grass on the edges of the dripline, also much quicker to mow my yard now.
BTW, I didn't buy mulch I went around neighborhoods with numerous live oaks and collected bags of leaves the residents left out for the city to pick up.