You can’t become President without being a good politician at least in some sense, but he ran against the guy who pardoned Nixon. And Ford botched the debate, claiming that the USSR didn’t dominate Poland.
And I don’t think it is accurate to say that nobody thought Carter could win -
His tactic wasn’t particularly unusual or novel - he ran as an outsider, untainted by the Washington scandals. He managed to win, of course, at least in 1976. Four years later, against IMO a better politician, he struggled against Ted Kennedy and then got spanked in the general election.
He is a better person than he was a politician, IMO.
One thing Carter did that forever changed presidential primaries is he made the Iowa Caucus relevant.
Other candidates didn’t really take much interest seeing little Iowa as pretty insignificant but he spent a lot of time campaigning in state, visiting all the counties, meeting the people, talking with them, listening to them and yes he even earned the trust of some people that to mitigate the lack of funds in his campaign they would open their doors for him to spend the night. Two years later every one of those people who did that were invited to spend the night at the White House at his inaugural ball.
It was what we now call good old retail politics and everyone does it now but he made it a big deal. And for what its worth he didn’t win the Iowa Caucus — he came second to uncommitted! However the difference between Carter in second to the third placed candidate was two-to-one therefore Carter was the “clear winner” of the Caucus and the media having pretty much ignored him for the last year suddenly latched onto him.
There was a Time Magazine double page feature circa 1975 profiling about a dozen democrats who could feasibly become the next president. Jimmy Carter was not included.
Jimmy Carter and his wife, Rosalyn, have also been married longer than any other presidential couple in history, 73 years, already beating George H. W. and Barbara Bush by a month.