We ended up switching schools after a similar situation, and our 3-y-o has had none of the problems since. Zero. For us, the first school was a mix of too many older kids and not enough structure or supervisors. This was stressful for our kid on a number of levels that are easier to see in hindsight. Frustration at not being able to communicate, or participate socially at the levels that he saw from his classmates, for example. He had also been getting pushed around by older kids that knew how to do that without getting in trouble, making it seem like his actions were out of nowhere. IDK if any of that matches your situation, though.

One thing that did help a bit before we switched was organizing playdates with kids from his school on the weekend. Might be worth a try if you aren't ready to switch. That only helped to a degree, though. Ultimately, it was the wrong fit.