I would get the ball rolling gathering as much evidence for an EHCP now if you have missed the window to appeal the refusal to assess.
Have you had any involvement from SALT, OT, paediatrician or other professionals? Any information from nursery to show he requires more support than OAP, any communications about incidents, reports etc.
Because for now your options are limited to mainstream or don't send him until you go through the ehcp process. He doesn't have to be attending school for you to apply, but there is the benefit of school being able to contribute their observations and assessments to support the request for a needs assessment that otherwise you wouldn't have.
In my experience although not a requirement, school themselves are very reluctant to request an EHCNA without having been through at least two cycles of assess, plan, do, review before they will considering applying for an EHCP themselves, and a lot if not all LA's have this as their policy to gatekeep school's EHCP requests (similar to the 6k notional spend) which are not what the law says is needed but still LA's will turn down as many requests as possible knowing not everyone will appeal.
However you can and I would suggest you do, make a parental request for the ehc needs assessment and alongside any medical and nursery evidence you have, also talk to the school about your plan so they can provide any extra evidence. Once he is on the SEN register any IEPs/support plans and one page profile etc.
I personally wish I had pushed for a SEN school but every child is different. Reception was fine with a high level of support but from y1 the wheels began to fall off. My son was non conversational when he started Reception but did have words, but significant phonological and articulation difficulties. Adhd and autism and dyspraxia with significsnt sensory processing difficulties.
The reason for mainstream not being the right place for my son was multifactorial. Firstly I regret home not having access to hogh quality onsite SALT and OT. Even with his EHCP the amount and quality of SALT and OT thry provided was poor. His DLA is used for private SALT and that is the only reason he can now communicate verbally.
The main reason MS was not right for himcis the sensory overwhelm of 30 children, the noise and business of the school. He needed a low arousal calm classroom and mainstream isn't that which led to refusal /ebsna.
He also needs a lot of support with learning and is working quite a few years behind age related expectations. He really wasn't able to understand or learn and was never felt a part of the class but like he was lumped in there as an outsider, without a friendship group and stuck with a full time TA whose job seemed to be to make sure he wasn't too disruptive.
The grand idea of inclusion and that mainstream will be the best education for all but those with the most profound SEND is a nice idea but in reality doesn't work for so many. Of course SOME children with SEND do thrive in MS with adjustments but many more do not. My experience was that the limited adjustments in mainstream on thr name.of inclusion were actually just small changes aim at firefighting the flames while the gas feeding the fire is still flowing. Giving regular breaks away from the whole class to regulate is not inclusion when thrle classroom is overestimating and busy.
My son is not every autistic child though and for your son he may thrive. If the school are well informed on his SEND from yourself and nursery I would see how he finds it while you request the ehcp. If school agree they are not able to meet his needs once you have the plan then you can review your options - every child has the right to a MS education if you feel that is what is best. Likewise if mainstream schools do say they can meet need it will be a fight to get specialist.
Good luck.