You cannot.

I used to work for one state's Department of Motor Vehicles.

Part of why REAL ID is such a charley foxtrot is because there exists no such identifier and since every state counts approximately as a sort-of-almost sovereign nation (this is basically what the 10th Amendment guarantees), there is and can be no possible nationwide citizen identifier.

There are about 3500 different counties in the US. All of which may or may not issue their own birth certificates. States are supposed to do that now.

To give a slightly more technical answer, at a large insurance company I used to work for, the legal department had provided definitions on what conditions we would consider various components of PII a match. So between SSN, DoB, First Name, Last Name, and a couple others, there were potential combinations that our system would say, "yes this is the same person". Note that we didn't necessarily need exact matches on things like names, but "close enough" matches were sometimes sufficient.

You can't.

That's why everybody use SSN.

The population health database I work with uses generated IDs for people and relies on health systems to link records before submission (they put a lot of effort into data used for billing). But we do check for problems by looking at duplicates of SSN with date of birth. We don't consider names, because they could be transcribed differently. Even though the SSN+DOB pair should be unique, there have been cases where a widow provides her deceased husband's SSN. Likely because she used it for Social Security benefits and forgot her own long ago.

You can get kind-of close with driver's license numbers. They will change when US citizens move among states, (and we do that quite frequently.)

(People who don't drive have to get state-issued IDs that have the same number. At least, they have to if they want to buy do anything that requires proof of identification.)

How about not doing that?

ha ha only serious; ask them for their papers and if they say “who the fuck are you?”, they’re americans!

a slightly more serious answer: you largely don’t. The US doesn’t have a national ID, proof of birth is not even close to standardized, etc.