Take every stereotype and cliche about Canada and Canadians you can think of and alter history so that their opposite is widely supposed to be true. Obviously you can go back to the voyages of discovery and you may have to.
As someone who lives in that region, I freaking doubt it would be possible. While we may be populous we have a reputation for being big into the military but also being the least organized province in the country. Everyone already gives Checagou a hard time for allegedly rigging multiple elections as a mid-size city, imagine if it didn't have the oversight from Ottawa or even Toronto and had major political influence.Figure out some way of having a different North American country control the territory to the south of the Great Lakes and New England. That'd rob Canada of a large chunk of its population, which in turn would make it far less able to be a major military power...and being a major military power is one thing everyone associates with the nation.
The first one that comes to mind is how obsessed everyone here is with the Canadian Royal Family, yet you know we'd hate to pay for them. Maybe if Queen Victoria didn't have 9 sons they wouldn't have had the bright idea to send some of the younger ones to start Kingdoms out of colonies. All I know is if a world without Prince Francis, Duke of Clarence means I don't have to hear about how "Princess Louise is pregnant with twin girls" for the 77th time, "Is this random girl finally the one for Prince Albert", or worst of all "Gin addicted Jane tries to force Queen Victoria II off her throne" sign me up.
(On the other hand, the sports rivalry between Canada, Australia, & New Zealand, initially fueled by Francis and his younger brothers Frederick and Augustus, wouldn't exist, which would make me irrationally sad, so maybe not).