I saw this question on a political forum, and realized the answer depends on what you mean.
It would be very difficult for a third party nominee to win the presidency in the current American system. A ticket with two moderate Governors got less than five percent against Trump and Hillary, the two least popular major party presidential candidates ever.
There are several systemic problems for third party nominees. Ballot access closes after the primaries are over, so independent candidates can’t make a decision after Democratic and Republicans have selected the nominee; they pretty much have to jump in before that, limiting their ability to take advantage of a divisive primary. If they don’t win states with 270+ electoral votes, the election goes to the House of Representatives, decided in an odd way (each state’s congressional delegation has one vote.) Those people will be political insiders who will have to explain to primary voters why they don’t go with the party’s choice if they go Independent, so they’ll want to stick with their guy. Early voting also starts soon enough that a third party nominee can’t depend on last minute support at the time voters start paying attention. By that point, a non-trivial number will have already backed the Democrat or the Republican.
There might be a sweet spot in which a third party nominee can win. The problem is that when the major party nominees are suitably unpopular, most voters aren’t going to go third party; they’re going to vote against the person they hate, just as plenty of Democrats went with Hillary because they loathed Trump and many Republicans held their nose for Trump because they despised Hillary. So you’d need a situation where voters aren’t enthusiastic for the major party candidates, but aren’t too worried about the other guy winning. And you’d need a third party candidate who isn’t just going to take votes away from one party, to just function as a spoiler.
That said, there is one way an independent can win. It’s by running in a major party nomination. Trump pulled it off, and Sanders came close (and if he was ten years younger, he would be the 2020 Democratic frontrunner). 19,743,821 votes in the general election got Ross Perot just under 19 percent of the popular vote in 1992 (and zero electoral votes.) 14,015,993 votes in the Republican primary got Donald Trump the party’s nomination, and that gave him a credible shot at the white house. When looking at that record, qualified independents are going to be less likely to run on a third party ticket, when they’d have a better chance winning as a Democrat or a Republican. Assuming their interests and political beliefs are aligned closely enough with a major party, they’ll be able to take advantage of the campaign infrastructure of the national party, as well as that of every candidate in the general election. And those guys will know that their fates are intertwined with the top of the ticket.