You have the right to queue for several hours and present your biometric passport to a human who will take your picture, save it to another database, and then visually compare that to your face.
Obviously other countries have their own rules.
The best example I can find is https://en.wikipedia.org/wiki/William_Worthy#Right_to_travel...:
“He was able to return to the U.S. in October 1961, showing his birth certificate and vaccination record at Miami Airport”
That’s decades ago, though, and he still showed something (but not something that realistically identified him) to get in.
You can show them any identification documents you do have, like drivers license, to establish your identity. For establishing citizenship, one option is if you previously has a passport (expired, or just not with you) then can look up that record, and if it is recent enough to pull up a photo they can compare to you that can also help.
Other ways of verifying citizenship depends on what databases they have access to. For example if they have access to the Social security numident database, they could look up a number to see the associated name citizenship flags. I'm not sure if they do though.
From what I have heard anecdotally is that it is usually not too hard to convince them if you really are a citizen (except in edge cases like being born abroad to Americans without parents registering your birth with the US.)
In any case they will formally warn you about it being illegal for Americans to enter without a passport (it is, but there is no punishment for the crime anymore). This is to deter you from doing this again in the future, as having a passport makes things much faster and easier for everyone.