Considering how it has the same internal borders (with the exception of Texas having Greer County), it looks like the US gobbles up these territories sometime after 1890, or following the Civil War at the earliest.
Maybe...
1) Liberia doesn't vote to be independent.
2) The US accepts the annexation of Yucatan
3) Texas goes neutral in the Civil War in exchange for Greer County and the US Civil War is shorter. The US thus has a larger population.
4) The Canadian Confederation fails, instead there being a Maritime Confederation and a United Province of Canada. This isn't that implausible considering the Canadians more or less invited themselves to confederation discussions OTL. Without a Canadian Confederation there's no trans-Canadian railroad and the US absorbs western Rupert's land (Alberta, Sasketchewan, Northwest territories of OTL) and British Columbia (who chose Canada over the US due to railroad promises). They also support Riel's rebellion, and Manitoba/Assinioba becomes independent US-aligned polity
5) In 1867 the US ambassador to Venezuela proposed annexing the country. Maybe the US does that here.
6) The Annexation of Santo Domingo goes through under Grant
7) The US grabs Puerto Rico and Cuba from Spain a bit earlier, maybe the 1870s
8) When the US intervenes to back Panama against Colombia, it instead ops to just invade Colombia and annex a chunk of the place. In order to make the Colombians feel better, they give them the Venezuelan interior.
9) The US sides with the Central Powers (butterfly net being used here) and grabs Britain and France's colonies in the great war. It annexes Canada, Acadia, and the caribbean colonies. It proceeds to bully Assinioba into joining the US. Assinioba is admitted as two states - Manitoba and Kenora. Plus the US grabs Sierra Leone.
10) Somebody convinces the Danes to sell greenland along with the Virgin Islands during WW1.
11) The Mexican Revolution is far messier and a lot more Mexicans move to the US. Between the US occupying large chunks of Mexico and many Mexicans in the US coming to appreciate their new country, the US somehow annexes Mexico.
12) Power-hungry Americans looking at an incomplete map say to hell with it and invade Central America and Haiti in the 1920s.
the general politics of the US must be jingoistic as hell and far less racist for all of this to happen.