Good question. One team that definitely comes to mind is 2016 Coastal Carolina, the No. 2 seed who shocked two top seeded teams (NC State and LSU) on their way to Omaha. When they got there, they battled through the losers' bracket after a second round loss to TCU, before beating Arizona to win the CWS title.
That's a really good one. In retrospect, they were a really talented team and maybe they weren't that surprised internally with how well they were doing. But still, I can't imagine they thought they'd win the whole thing.
Yeah I agree with you. Just goes to show how key keeping the mindset of "take it one game at a time" really is, especially in the NCAA Tournament. They had to survive multiple elimination games, which is not easy to do either.