If you are poor enough you can qualify for Medicaid (MediCal in California) which is a sort of limited health insurance. This is life saving for poorer families and most of the time completely covers birth costs. After birth in some states they even offer follow up plans from nurses for assistance with food and meal plans for babies and toddlers.
Even if you don't qualify you can apply for financial aid which I believe is required to be offered in every public hospital even to people whether citizens or not. If not you can just take on the debt and not pay, which destroys your credit score but after long enough you might be offered a favorable financing or a discount... Only after being harassed by collections for months if not years.
Source: not American but I've worked with American healthcare workers interpreting for Spanish.
That would work with me lol