There are almost never seedlings growing from acorns. If there were, you would be able to pull them up easily. What you see are sprouts from the roots of the existing tree; therefore, you do not want to spray a herbicide on them in an attempt to eliminate the sprouts for you will hurt the “mother” tree along with the sprouts.
Only a small percentage of oaks send up suckers from the roots. It is a genetic trait, like freckles, except I like freckles. But like freckles and sunshine, some trees have the ability to sucker, but do not unless stimulated to do so. Oaks having a slight tendency to sprout suckers will often do so when roots hit a barrier, such as trees confined to a parking lot planter, or between a sidewalk and driveway. Also, when roots are disturbed and damaged by rototilling, they are more likely to sprout suckers. But some trees never will make suckers. When choosing an oak in a garden center, if there are sprouts coming up at the inside edges of the container, I would avoid that tree.
You may choose to mow them along with the grass, if grass still exists. Or if the grass has thinned too much, you might plant Asiatic Jasmine groundcover, and use hedge trimmers to trim the jasmine and oak sprouts to a uniform height. You can cover the area of sprouts with a heavy gauge woven geotextile, and then either mulch or spread large gravel or decomposed granite over the top of the geotextile. My favorite solution, when appropriate, is to cover the ground with geotextile and then build a wood deck.
Or if you prefer a thick green lawn, you may remove the oak tree, and all of the tree roots with a backhoe. If you just cut down the tree, grind down the stump and all the large roots you can see, there will still be thousands of oak sprouts emerging from the remaining roots in your new lawn or bed area for a few years afterwards. The area will need to be continually sprayed with an herbicide.
James 
Susan Bradshaw says
I’ve tried Sucker Punch on some of the thousands of live oak sprouts in my yard, without meaningful results. Like some other readers, only one tree (I have 5 live oaks) produces these little devils. This one tree has a concrete fish pond, a sidewalk and a driveway at its base; hence, the proliferation of suckers. Weed whacking only serves to “prune” them and they grow back bushier than ever. I’m going to try vinegar, and continue to hand-pull the suckers and the roots on which they sprout. I can fill a Lowe’s bucket full to the brim in about a half-hour. But the mature trees are lovely, and also protected by City ordinance.
Rosemary Willfong says
We simply have adopted the practice of having our gardeners weed eat any volunteers that come up each week.
The issue with Oaks, is that they are just like people who are born with various characteristics. One of those characteristics with a Oaks, is that some trees are genetically pre-disposed to throwing volunteers. It does not mean they are not a great tree! To solve the problem, you find a way to dispose of volunteers early and just as soon as they arrive. This you do, in order “not” to have to ever deal with the hard wood that sets up after a few months. Religiously, when we mow now, our gardener weed eats all volunteers. If you have too many (of course) this may not work. However, although the area where we have volunteers is pretty large, it only takes a few minutes to weed eat if you do it each week? Anything else you do may jeopardize the tree or another one close to it? We have tried several ways to get rid of them and in the end, you learn it is best to just “live with it!”
All I can say, is that we are blessed to have great gardeners who do this for us. At first, they too balked! – but they soon learned it is easy if you just do this each week.
Jesse Jenkins says
Well said! Staying on top of mowing or weed eating them is a good strategy.