The Briton had braced himself for a tough time in hauling Mercedes up the grid, but has already delivered two podium finishes and one pole position so far.
That run of form has put Hamilton in a position where he can contemplate a title challenge, but he says his mindset of simply chasing a single win remains unchanged.
When asked by AUTOSPORT about what had changed for him after his positive start, Hamilton said: "It is just the same thing as we had coming into the season.
"It is far too early to start thinking about the championship. The fact that we can say we are even in the group that is fighting for the championship is a big bonus for us.
"We will have the same approach. We are trying to win; the approach we were having before was trying to win, and we have to take it one race at a time to try and improve."
Hamilton says that the only thing that has changed for Mercedes because of the situation it is in, is that further improvements will be much harder to come by.
"The guys are trying as hard as they can, so obviously if we were further back it would be easier to make bigger steps," he said.
"Now we have a car that is quite competitive it is harder to make steps, improvement steps.
"But the guys are pushing just as hard, but perhaps they have more force behind them from the likes of Ross [Brawn], Toto [Wolff] and me."