"a 'papa' for the city of Rome?"
The first Pope arrived in Rome in the first century. The title we apply to the office came later, but the office was there.
Your logic seems similar to saying there was no Greenland until someone named it Greenland. LOL
Greenland has been there for millenia, under many names.
I think that you’ll have an easier time understanding my posts on this thread when you realize that I am saying that, before the sixth century, PM and “papa” were not connected in Rome or anywhere else. I’m fully aware that the city of Rome had Chrsitian leaders long before Constantine became the first Christian emperor.