What steps would have to happen within the United States government for a third party candidate to someday win a presidential election?

The United States government would most likely need to change its voting system drastically for a third party candidate to win the presidency. Known by political scientists as Duverger’s Law, the way officials are elected in the United States creates and continues the country’s two-party political system. The American winner-take-all election system with one legislative seat per district supports—and practically guarantees—having only two dominant parties. This contrasts with the proportional representation systems of most of the world’s democracies. In many countries, citizens vote for a party who receives proportional representation, allowing various political groups with diverse platforms all to have a voice.
One way a third party candidate could conceivably win a presidential election is if a large number of voters defected from a traditional party to a new, formerly third, party. There is historical precedence for this sort of action. Abraham Lincoln’s election was the last time a third party candidate won the presidency, establishing the Republican Party in place of the Whig Party.
American voting systems would also need to be changed dramatically just to encourage more third party candidates. For example, a system called Approval Voting would allow people to vote for as many candidates as they wished. This way, the person with the majority of votes still wins, but votes for third party candidates do not unintentionally reward the opposition.