Ok, well regardless of diagnosis which in the current times is taking years anyway, best thing to do is pursue that route but also look into what supports he needs anyway.
whether he has SEN or not, the important thing to do is work out what is triggering the violence/disruption and then change the environment so that it isn’t there. You/the school can then work on developing his tolerance to it.
the free-flow classroom sounds tricky. Many kids in that kind of situation prefer either a much more child led environment (think forest school and no adult led activities at all) or a completely adult led environment (all kids at desks and get in with what the teacher tells you). The mix can be confusing for some kids and make them very anxious.
what was he like at pre-school/nursery? That will give you some clues.
more specifically, the EP would probably ask the teacher to fill in an ABC chart. This is a way of working out what is triggering the disruptive/violent behaviour.
so every time he is violent/dusruptive the teacher writes down:
A antecedents. What was happening before the behaviour started. In as much detail as possible.
B- behaviour. Write down what the behaviour actually was, so what happened. Again, detail is Important.
c - consequences. So this is writing down what happened after the behaviour. Not consequences as in punishment that the school or you impose but just what happened as a result of the behaviour.
so an example might be:
A - the class were lining up to go to assembly
B - the child kicked the child. Next to him and then threw a chair at the teaxher
C - the class were late for assembly and the child didn’t go in to assembly.
this sort of analysis helps understand what precisely your child is finding difficult and then support/exemptions can be put in place.