Based on your lower comment, Rhode Island.
Median family income $87k
Cost-of-living ~$36k excluding housing
With your example of a $350K home, someone making the median (presumably not 20-30 year olds but more like 40-45 year olds...) they could save up the $70k down payment in under 2 years.
P & I payment of ~$2k / month. Maybe $1k more for escrow of taxes and insurance.
So $72k total cost of living on $87k, assuming you've made it to median income.
Of course, if you're making less than $72k, buying a $350k house would simply be... untenable.
Also, based on rough guideline of "30% of income on housing", you'd definitely want to keep your mortgage under $2200 / month.
Census link indicates median home values are closer to $404K though, too.