Well, considering the fact that "heritability" is a measure of how much of a given phenotype's expression is due to genetic variation, probably not soon. "Heritable" is not a word used to refer to environmental factors such as parental care and upbringing. In studies on heritability of specific traits, these environmental factors are used as classifications for broader observations of genetic variations (for example, in twin studies, was twin pair A raised in the same household like pair B?).

Going back to autism specifically, the Simons Foundation Autism Research Initiative identified a single genetic mutation that accounted for 25% of diagnoses in their Simplex Collection[1], while the other 75% were impacted by 200-400 different genes. This data is available online as of 2016[2], though some analyses may be paywalled.

[1]: https://sfari.org/resources/autism-cohorts/simons-simplex-co...

[2]: https://www.simonsfoundation.org/features/foundation-news/si...