my eldest dc had the 1st mmr jab late as had been ill when should have had it - was around 18 months iirc
tbh we were never entirely comfortable about it as I have a family friend whose DD was damaged by immunisation a few years earlier and developed epilepsy and other issues after mmr and will now never live independently
we felt dc was not same after and subsequently had speech issues with sounds that should have developed around age 2, requiring input from SALT during nursery/reception, and does have some social issues now that really became an issue from y5/6 in primary school - academically, no issues, DC is generally top sets and performing extremely well in our local state comprehensive, and doesn't exhibit enough traits to be assessed for ASD
Because of this, we chose not to give the pre school booster and not to immunise dc2 against mmr - dc2 has none of those issues, although both dcs have had all other vaccinations in line with schedule
If you believe you DC has been damaged, I believe the best thing you can really do now is to ensure you get a diagnosis of issues/needs and as much help as is available to assist with developing life skills and coping at school - and get the best information to help you decide about further vaccinations
Personally, I don't feel you will get very far in trying to prove the link one way or the other, nor achieve much by it.... my focus is very much on ensuring my dc has the best outcome from school and is prepared for life in general...
It is unlikely we would ever know for certain what caused these issues, and I am not sure that will help any of us... what matters is that our dc is happy and able to get the most of out life with help when needed