People with autism are born with it, so it's likely genetics. As for the factors that contribute to said genetics, who knows? Some people like to argue that modern life has created the toxins that cause autism (plastics etc) but there's no proof that autism didn't exist before modern civilization. They just didn't know what it was and probably just thought it was caused by a magical curse or something.
The thing with correlation is that you can't proof causation, so while more autistic children are born by older parents, there are also autistic children born by younger parents. Older parental age is also correlated with Down syndrome and other conditions, so it should probably be looked into, but definitely can't be isolated as the single cause.
And vaccines 100% does NOT cause autism, just in case anybody still thinks that for some reason.