If you do a bit of research you quickly discover that the reason for huge increase is unknown.
See:
cdc.gov/ncbddd/autism/research.html
And also:
ninds.nih.gov/Disorders/Patient-Caregiver-Education/Fact-Sheets/Autism-Spectrum-Disorder-Fact-Sheet#3082_5
In my own opinion one reason is advanced parental age.
As for vaccines, as I say my sister is a nurse. There are particular vaccine she, and other medical professionals she knows, have some concerns about. Note, that they are not concerned about the 'core' vaccines.
In everything there is a weighing up of risks. Perhaps you end up with more cases of autism (or more severe cases of it), but the cost is worth paying because of what the vaccines prevent. The conundrum here is will medical leaders acknowledge vaccines have a downside? If they do, even a little bit, and people lose faith in vaccines, you would have less autism for example, but other horrors might start to creep back into to our populations.
Consider that for many years flouride was considered not just safe but fully advantageous by various governments. And now, many governments have banned it from public water. Why?
Sometimes governments allow things they shouldn't and it can take years, even decades for the realisation to dawn.
In any event vaccines might be only one among several causal factors. One last thing, my own 'anecdotal' experience: growing up in the seventies I suppose you might know one kind who had mild symptoms, but today I look around me and there are more severe cases. You cannot miss it. Had the same level of these severe cases existed in say the seventies, it would absolutely have been noticed. We might have been innocent about many things (including vaccines?) but we were not zombies who didn't notice such severe cases. Even in my own extended family there are three cases of bad autism. Not just mild symptoms. Children who find it very hard to function normally. When the kids are at a family gathering everyone cannot help but notice something has changed. At similar family gatherings in the past, you did not have all these severe cases. It is as simple as that.
You could argue that 'special' children were all kept locked up in closets in the seventies? No! I had plenty of cousins back then, and none were locked up. We would have known. People talk and gossip. The truth in my experience is that there are more severe cases today.
I wonder is it the same globally, or just in particular regions?