The New Democratic Party in Canada has been a weirdly successful third party at times with so what would be the best way to have them secure a full win in a Canadian election? The best point I can see is back in 2011 when they came in second with 30% of the vote but it seems like a fairly steep hill to climb to beat Steven Harper.
How can the NDP win a Canadian parliamentary election?
Something really bad happens to the Liberals and NDP manages to capitalise and become the main left-wing federal party in Canada. They eventually manage to win an election after being HM Loyal Opposition for a few Tory governments.
Elizabeth May and her Green party steal a few more seats in the West While Steven Harper gets A Few more eggs in the face over policy . A young Justin Trudeau campaigns on Voter Reform and sticks with it and Jack Layton doesn't die of cancer.
I got a TL that deals with this exact topic. Likely your best starting point is the 2015 election.