"A century ago you could go into any store and just buy a gun with a handful of cash and never mention your name."


Actually, that was the case in many areas in the USA until GCA 1968 came along in the wake of the JFK assassination. Some cities and states may have had laws requiring recordkeeping for gun sales before then, but most required no paperwork, just like buying a candy bar. About the most paperwork that would happen was for the gun store to write you a sales receipt.

Your chances of finding out who the original purchaser was are very slim.