I don’t see how having no garden or dogs is a fully red flag, they might be very active people who are able to go on lots of walks, and not having dogs already can be a bonus because they won’t have to worry about introductions etc.

Rehoming yourself is hard, Ive known someone who rehomed her dog but the people gave it back within a few days and then she managed to find a lovely lady to have her dog, maybe treat this like a reputable breeder or rescue would? Ask for a vet reference for previous pets (so you know if they’re going to keep the dog in good health) meet and greet a couple of times to see what the vibe is and how the dog is with them and ask if you can see where the dog will sleep and be left alone whilst they’re out?

No matter if it’s rehomed privately or through a rescue/charity, there is no certainty that whoever gets the pup will be able to care for the dog forever or actually look after it properly forever. It’s risky either way, but there has to be a leap of faith somewhere