The Tynecastle men start the campaign 15 points behind the rest of the teams in the Scottish Premier League after the club entered administration.
Hamill believes the youthful squad are gelling in time for the first match of the new term against St Johnstone.
And the former Kilmarnock full-back insists the belief throughout the dressing room is that Hearts will stay up.
Hamill said: "We're happy enough to be underdogs. Hopefully, come the end of the season, we can put that right and make sure that people will be talking about the boys doing themselves justice.
"This season is one that I'm looking forward to. If you ask anybody in the dressing room, it's one we're all looking forward to and we see each game as a cup final.
"If we can stay up then I'm quite confident that it'll be the biggest achievement in the club's history.
"It's going to be a long season but hopefully the young boys can continue to progress the way they have been. I don't think we'll be far away."