We didn’t have saving, either, used it for private hs (owing to issues with the local public.) An expensive area, though nowhere near what NYC costs.
We used income, the kids took the student loans, but we did take modest Parent Plus loans. (Very modest, in comparison to what some tell.)
My caution is always: no more parent loans than you can project paying back in a few years. We knew the larger income was secure. We knew we could afford the rest of living expenses and the payback.