QBs who lost their first Super Bowl before winning it?

[TecmoBengals]

I was curious to see what NFL history reveals about the career trajectory Joe Burrow now faces as a QB who lost his first Super Bowl game. Specifically, how many QBs lost the game in their first appearance, but then made it back to experience the ultimate NFL victory by winning the Super Bowl? I only focused on players who lost at their first attempt before winning it at least once since this is the situation applicable to Burrow.

Is it a small list of only 4 QBs? I don't think I am overlooking any QBs matching my criteria.

Len Dawson lost in 1966 before winning in 1969 - 3 year gap (1-1 overall).
Bob Griese lost in 1971 before winning in 1972 - 1 year gap (2-1 overall).
Roger Staubach lost in 1975 before winning in 1977 - 2 year gap (1-2 overall).
John Elway lost in 1986 before winning in 1997 - 11 year gap (2-3 overall).

Including Burrow, I count 30 QBs who lost the Super Bowl without eventually experiencing a win. Some had multiple shots at winning it including Tarkenton who was 0-3 and Kelly who was 0-4. Burrow joins Cam Newton, Matt Ryan, Jared Goff, and Jimmy Garoppolo as active players working to overcome their 0-1 Super Bowl record to get a win. Among the active group, I think Burrow is in the best position to become the 5th QB to start his Super Bowl career 0-1, but has a possibility to return and win the game.

History does reveal it is a difficult task. Please let me know if I am overlooking any QB that started 0-1, but then won the Super Bowl.

What is it going to take to get back to the Super Bowl and win it all? Is it as simple as fixing the OL?