Get his hearing and eyes checked to rule out any difficulties with those senses causing frustration etc. Just because we think they are fine because they can hear a biscuit packet rustle in the kitchen when they are upstairs doesn’t mean a child isn’t having difficulties hearing at different frequencies (we have had this issue with my DS, who has glue ear).
All behaviour is communication. My DS(9) started nursery at 3 and quickly went from being very well-behaved prior to this to being almost constant low-level disruptive and pushing other kids, knocking over tower blocks, putting a foot out to trip another child over etc. He never bit or was plain nasty - it was what the nursery called low-level behaviour.
Eventually the nursery asked our permission to get an Educational Psychologist assessment done as they couldn’t establish why he was behaving like this when it was very out of character. The EP assessed him 3 times total and the outcome was that he was anxious about the unpredictability of the nursery environment, and that the behaviours were to try and communicate with his peers. The EP suggested a number of strategies to put in place to help DS feel more secure and to teach him more tools for communicating in an age-appropriate manner with his peers. We quickly saw results and the behaviours stopped, with only a very occasional incident about once a month. So, what I’m trying to say is ask the nursery about them getting an EP in (they may push back due to funding, if so see if you can organise and pay for one yourself). Now at age 9 DS is very well-behaved at school and clubs etc, and is actually a bit the opposite and tells me about how annoying it is when other kids misbehave!
Another side of the coin is a former friend with a child the same age as mine who never gave him boundaries or consequences, no matter where he was or the situation. Her child would attack mine and she would do nothing but occasionally simper ‘aww that’s not nice darling.’ The child is now horrifically behaved and she is a former friend for a good reason (I’ve heard this through a mutual friend).
So, you have two routes you could take - get advice and help now, or be that parent who ignores poor behaviour and simpers to their every whim. You are not too late at 3 so push for help, and keep pushing until someone listens. Never give up on your child.