In 63 BCE, well before he was famous, Caesar stood for the office of pontifex maximus against two senior former consuls and won it. The post was for life, it carried the official residence on the Sacred Way, and it made a politician in heavy debt the head of Roman state religion at the age of thirty seven. He held it for the remaining nineteen years of his life.
The office was not primarily about belief. The college of pontiffs supervised the calendar, and the Roman civil year of 355 days needed an extra month inserted at intervals to keep it in step with the seasons. The decision to insert it was theirs, it was made or withheld for political reasons as often as astronomical ones, and by the middle of the first century BCE the calendar had drifted roughly three months out of true, so that harvest festivals fell in the wrong season.
Caesar fixed it with the advice of Greek astronomers, among them Sosigenes of Alexandria, by abandoning the lunar basis altogether. The reformed year ran 365 days with a single intercalary day every fourth year, and to reset the starting point 46 BCE was extended to 445 days, the longest year in recorded history. The result was accurate to about eleven minutes a year, which was good enough to stand until 1582, and the month of his birth was renamed for him. A priestly duty, discharged competently, turned out to be the most durable thing he did.