The water seems to be getting muddied here by people referencing cases of extreme violence in reception settings and comparing this to OP's sons settling in experience of one instance of biting and 3 occasions hitting another child.
Let's be clear that any school's response to these two wildly different behaviour patterns would and should be very different.
And yet we have @Florenz wading in basically saying that only children with completely perfect behaviour deserve an education in mainstream school!
Which would be marvellous if we had a super well funded education & children's services system, but we don't. Funding for special schools was cut donkey's years ago. Funding for SEN support, CAMHS and assessments has been squeezed ever harder over the last 12 years from Conservative austerity cuts. School budgets are under more pressure than ever before this academic year, so most are having to cut TAs and LSAs to pay the heating bill, even when there are children whose education (and that of the other 29 in the class) would clearly benefit from that additional adult in their setting.
As taxpayers, we have (nationally) voted for this, condoned this approach to education, and returned a government making these cuts time after time.
Voters like @Florenz no doubt think that an approach that only suits the 'normal' majority is absolutely fine. Voted for by the able majority. But what happens if that child that is kicked out in the first term? There is no school place for them without an assessment. Assessments are taking well over a year in most parts of the country. Does the OP give up work to home educate? Claiming Universal Credit for unemployment, housing costs and carers allowance? Does the child bounce from pillar to post until they are in prison needing 3 paid wardens to cover a 24 hour rota because they've been unable to learn how to be a productive member of society in the education system?
Or is the investment of an additional LSA in the classroom THIS term the best investment taxpayers can make in OP's child? We've heard examples in the thread of amazing EYFS teachers picking up hearing loss, autism, ADHD and more by observing childrens' trigger points well.
A bite or kick from an overwhelmed 4 year old is NOT the same as 'terrorising the classroom'. I thought my own summer born would find Year R a doddle after four 10 hour days at nursery. At the end of the first week they bit ME - an outlet from a massive environment change where they are required to do exactly what they are told for 7 hours straight, with far fewer freedoms than in nursery, with tasks they are often enjoying taken away from them arbitrarily because 'it's time'. My child is developmentally 'normal' by the way, but summer born.
I'm lucky it was me not another child & I adjusted my expectations & out of school plans accordingly.
Sure, schools need to act swiftly in the interests of ALL children if a very violent child presents in Year R with no previous intervention history or support.
Teachers also need to pay attention and help young Year R pupils struggling to settle, which is the description OP has given - and multiple EYFS posters on the thread have given examples of best practice on how teachers and schools can help eliminate agressive responses through good classroom practice and supporting the child having difficulties.
Good support should ensure no other children are hurt once it's in place. De facto, if other children are still getting hurt, the school has not yet provided adequate support. Once they are at multiple support interventions and 2-1 adult support/restraining, sure there should be plenty of evidence that, at THAT point, mainstream education is unlikely to work, and fast tracking for special school should be underway.
I notice that none of the 'kick the kid out' posters have commented at all on the fact the teacher has recently relocated from private school. I'm not one for teacher bashing, they have a huge workload. But in OP's scenario, we do need to consider that the teacher might be so bad they they have already lost their job in a small class size private school. And is now completely out of their depth with a mixed ability state reception class of 30, including one child who needs a bit more attention and help to settle in to new routines without blowing a gasket.
It is entirely possible it is the teacher that is the problem rather than the child in OP's scenario! Mull that over @Florenz...