I'm not sure how any genuinely useful studies can be made on this yet, given the vast number of cases which are still missed.
It's not like Down syndrome which can be very clearly identified without fail, thereby making it possible to draw clearer causative links between the age of the parents and risk.
It may be that the children of younger parents just haven't been identified yet. Some children don't get diagnosed until they are in their teens. And some children - especially girls - don't get diagnosed at all.
Until there's a far more consistent and reliable method of diagnosing autism, any links to causative factors is primarily just speculative.
A pattern of inheritance is the single thing that seems to come up time and again, so there's an increasing belief that genetics is one of the most common causes. But again, without the fuller picture on diagnosis, it's really just an idea, nothing more.
I'm autistic and my two DC are autistic. I strongly, STRONGLY suspect my mum is autistic, but she's never been diagnosed. I also think my brother is autistic.
I was reading some research a little while ago which was referencing the possibility of there being identifiable differences in the brain MRI of autistic people. If this were to be the case, it would make it much more accurate to diagnose and then carry out more accurate research into common factors/risk factors. We're not "all a little bit autistic" as sometimes is claimed - the autistic brain is believed to operate in a very different way. This might be the route that leads us to better diagnosis and in turn, more accurate understanding of the cause.