Funny you should ask that... Let me offer a quick and very partial introduction on how the Roman state religion was organized.
It's not a Pope, it's a Supreme Pontiff
One of the titles of the Pope, Bishop of Rome, Patriarch of the West, is Supreme Pontiff, Pontifex Maximus (or Summus Pontifex) in Latin.
This title is old. Very old. As in, very much older than the Catholic Church or Christianity in general; and it has always been the title of the Great Priest of Rome, pagan or Christian.
At the top of the organized Roman state religion, back when Rome was pagan, was the College of Pontiffs, Collegium Pontificum; its members were the highest ranking priests of the state religion; it included the Rex Sacrorum (King of Sacraments), the fifteen flamens (high priests of the individual cults of Jupiter, Mars, Quirinus -- the flamines majores -- and 12 other deities -- the flamines minores), and the Vestals. The Pontifex Maximus was the head of the College of Pontiffs, and thus the Great Priest of Rome.
The title was carried over to the Christian Great Priest of Rome; there has been a Pontifex Maximus in Rome for 27 centuries now.
Aside: the word pontifex definitely looks like it should mean "bridge-maker". Lots of mental energy has been expended trying to understand why the Romans called (and still call) their Great Priest the Supreme Bridge-Maker, whereas actual bridge-makers were never called pontifices.
Left, Octavianus Augustus as pagan Pontifex Maximus, 1st century BCE. Photograph by Marie-Lan Nguyen, available on Wikimedia; public domain. Right, Pope Clement XI as Christian Pontifex Maximus. Engraving by Christoph Weigel the Elder, 18th century CE.
The way the Pontifex Maximus was appointed changed in the course of history.
Originally, he was elected from among the members of the College of Pontiffs, and he had to be a patrician.
Then (in the 4th century BCE) the election became public -- the Pontifex Maximus was elected by the people, and the office was opened to plebeians.
Then (in the 2nd century BCE) the office became overtly political -- the Pontifex Maximus was elected by the comitia tributa (the assembly by tribes), just like the consuls.
Then (in the 1st century BCE) the office was subsumed to the imperial power, one of the offices cumulated into the position of the man whom we call "emperor" of Rome.
Christian Pontifices Maximi are elected by the College of Cardinals. Even that changed during history, but I won't enter into details.
The Roman pagan state religion did actually have such a position. The Great Priest of Rome was called the Pontifex Maximus or Supreme Pontiff and he (it was always a he) presided over a College of Pontiffs containing the highest-ranking priests of the cults of individual deities. The title was carried over to the Christian Great Priest when Christianity became the state religion.