The hero is born into universe populated by similarly looking to him people. But he suspects he could be immortal and possess some (maybe, passive) special powers.
The facts known to him:
He ages slower than other people (still ages).
But he can receive not healable damage, scars do not disappear.
His reasoning and mentality is way different from other people, like between a robot and a human. He seems to outsmart all other people he had met in science and logic, still he cannot find a woman or a close friend because all people are scared of his way of reasoning and logic.
The society has a prophecy of a messiah or god coming with characteristics similar to that of the hero. Before his birth the rulers tried to kill all babies with similar characteristics, but unsuccessfully. There is a lot of people believing the prophecy but the downside is that all such prophecies of the local religion turned out to be wrong historically.
The society exists for a very long time, millions of years unchanged but with his birth dramatic changes came to the society.
Currently the hero has a strategy to just live as other people and see whether he will outlive them. Is there a better but not risky way to test whether he is immortal or has special powers?
The type of immortality he wants to check is like "divine intervention": if someone wants to kill him, the killer gets a stroke or changes intention or has his gun jammed, all seemingly in line with physical laws but not entirely. He does not want to risk testing it though.