I apologize for this delayed reply to your gardening question and hope it is still helpful to you.
Some of the sprouts could be from acorns but a lot of them under an oak tree are root sprouts. There is little you can do except mow them back. Planting a groundcover such as Asian jasmine will help conceal them but you'll still have to trim them off above the groundcover.
Thanks for the question. Best wishes for a wonderful gardening season. Please stop in again soon!
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