Honestly I just assume that those two are where people dump cars, I would never buy a car from either of those without an independent checkup or a warranty.

Also, the initial screening is not the only inspection that carmax does, if the issue is as pronounced as OP implies it’ll probably get caught and sent to an as-is dealer auction where people know that crap cars are sent.

See if Carmax will make you an offer. If it’s not bad enough to be blowing blue smoke and the coolant is clean, you may by able to sneak it by an underpaid intake tech.

If you do use CL or FB marketplace, don’t offload it without a word of warning please. People are struggling right now and the ones buying $400 cars are doing so because they can’t afford anything else. Carvana and Carmax are giant corporations so no moral issues with offloading on them.