The Lions face in-form Super Rugby side Crusaders on Saturday after narrowly beating Provincial Barbarians and losing 22-16 to Blues.
Wales wing North, 24, is one of four Lions making their first appearances of the tour in Canterbury.
"It's all about building for the Test series but we need to start kicking on now," North said.
"After this everyone will have had some game time so everyone's foot is in the door and playing now and I think we can kick on."
North scored two tries in the 2013 series which saw the Lions beat Australia 2-1 - their first Test series win in 16 years.
The Northampton Saints player sat out the opening two matches along with centre Jonathan Davies, scrum-half Conor Murray and flanker Sean O'Brien.
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North said he was carrying a "bump" when he arrived in New Zealand, but admits it was not easy watching from the sidelines.
"The Lions is the pinnacle and to not feature in the first two games is annoying because, like anybody, you just want to play," added North.
"But it's just part of touring isn't it? It's the bigger picture now, I knew I'd get my game time as and when and I just have to trust the medical staff and trust Gats [coach Warren Gatland] to make those calls and just be ready for it."
Crusaders are the form team in Super Rugby this season, with 14 wins in as many matches and field a team including eight All Blacks against the Lions.
North said the quality of the opposition has been no surprise to the tourists and believes it is better to be tested early on the tour than have the relatively easy introduction they had in Australia four years ago.
"We always knew the first few games were going to be ropey and not how we want to play," said North.
"And I think that was evident in 2013 as well, even though at the same stage we'd won two out of two the performances were not what we'd hoped for.
"I think the way we are now is probably better.
"You want to be tested in every game don't you? If you get that you become a better team as you go along."
And the much-talked-about itinerary means Gatland's men have no time to rest. They face Highlanders on 13 June before the Maori All Blacks on 17 June.
Those games are followed by three Tests on consecutive Saturdays against world champions New Zealand, which are North's targets.
"For me and with an eye to the the Test series I have to make sure when I get my chance I play well," he added.
"It's not just about the wings against us but quality wings we have in our own squad.
"I have to make sure I take my chance and really kick on."
George North believes the British and Irish Lions must "kick on" after a tough start to their New Zealand tour.