Scott Johnson's side have won just one of their four matches so far this season, as they prepare to face Wales in Cardiff on Saturday in their final game.
They were labelled the worst ever Scotland team by the former England manager Sir Clive Woodward after their 20-0 humiliation at the hands of the Auld Enemy at Murrayfield. But Hamilton sees progress after the Scots came within 90 seconds of beating France last weekend when Jean-Marc Doussain's late penalty stole a 19-17 victory for Les Bleus in Edinburgh. Hamilton, 31, knows time is running out for him to claim a Six Nations winner's medal but is not giving up hope yet.
The Montpellier lock said: "We've had to go to some dark places, especially after the England game. We know we didn't play well. It was a shocking day at the office.
"We have had to believe in what we are doing to come out of those places and the coaches certainly believe in where we are going.
"We've isolated ourselves in the squad so we can stick together and make sure we keep everything in-house, pulling in the same direction. You could see in certain aspects of the France game that we are definitely going in the right direction. Maybe a lot of supporters are getting sick of hearing that but as players we want that consistency and we want to win games.
"I am getting on a bit now and my ambition before I finish playing is to win a championship. I wouldn't keep coming back, leaving my two kids and wife at home in France, if I didn't believe in this squad.
"I genuinely believe we are getting closer to the point where we can challenge. I know people have heard it all before but if we keep putting in performances like we did against France and keep believing in what we are doing, there are a lot of young players in this squad who can take us there."
Tim Swinson's foul on Alexandre Flanquart as the clock was ticking down against the French led to Scotland conceding their 50th penalty of the tournament, more than any other country involved.
Johnson, the Scotland head coach, claimed he was concerned by that statistic but Hamilton refused to criticise referees.
"No-one ever agrees with the ref if you lose. If you win, you say he's done an alright job," he said.
"It's not about bagging the ref. They are their own people. They are not going to have the same views on all the permutations of the game. Some will see a scrum go down and let us carry on, others will ping it.
"We have to adapt to that. It's the same for both sides and I'm not going to say the referee is the reason for us not winning.
"We were comfortable against France at times and we have only ourselves to blame."
Hamilton is confident Scotland can shake off last Saturday's disappointment to win in the Millennium Stadium.
He said: "Going down to Wales will be tough. They are the reigning champions, a fantastic team. The Millennium Stadium is an unbelievable place to play in.
"But we are going down there with the mindset of winning the game. That's all we can do. We are disappointed with result last Saturday but will go to Wales and give it our best shot."