Going for broke by running a presidential candidate is a surefire way to lose, and no one really donates to parties that lose. Which is a problem, because presidential campaigns cost a crapton of money; Bernie 2016 cost $220M and that was the primary.
If you look at successful third or fourth parties in FPTP nations, they are generally running lots of local campaigns, which are cheaper, give a place to train a talent pool, and also show voters proof that they can get a job done. I don’t think I’ve ever seen a formal third party running for local positions near me. And in this role they can serve as kingmaker; they may never get the top job, but in a perenially razor-thin Senate margin and a currently thin House margin they could certainly lord a lot of power even with a handful of seats.
This is the end result of decades of gerrymandering.
Maybe a good metric would be the ratio of primary ballots cast to general election ballots cast. If a small number of extremist primary voters are de facto selecting the candidate that will win the general and get the "safe seat", that suggests an opportunity for disruption by being a high profile 3rd party candidate who's just a bit more moderate than candidates the extremists select (more appealing to the median voter).
Another idea is to reach out to a bunch of independent candidates and try to recruit them for your new party to work towards critical mass.
Look at the Tea Party and the DSA; they have enough motivated bases to form parties of their own, but their strategy is to co-opt and purify the existing mainstream parties. Equivalent movements in Spain decided to make their own parties and Podemos and Vox became the next two largest parties in Spanish elections.
It's not like party establishments haven't had candidates lose despite all odds. And Independents have had good streaks at lower offices (e.g. Bernie Sanders, Michael Bloomberg)
I wonder if there's anything to be learned from those weird "secondary" parties you see in some states. It will be like "Working Families Party" or whatever, with a Democratic or Republican candidate for President and few unique of down-ballot names.
I'm not sure exactly how those work. Might be just a way to use some legacy "default ballot access" In my state, a candidate supplied by any of the four largest parties would get on the ballot, even if only 15 people actually voted for the Green or Libertarian.
Electoral margins, particularly in downballot elections, are very very slim. For City Council of New York, which is a fairly powerful local position, you are looking at margins in the hundreds or thousands of voters, and combined with how thin legislative majorities tend to be, can form a significant wedge to wield.
It's more than that: The Democratic - (and arguably the Republican party at one time) - are functionally "big tent" parties. For example, the Democratic party has a progressive faction, an "establishment" faction, and a centrist/moderate faction.
These groups often have little in common. Just look at trumps support base.
The reason for that is structural. The Democratic and Republican parties have structurally built themselves into the election system in a way that shuts out any attempt to gain traction by third and fourth parties.
Just think about the fact that the Federal Election Commission, the organization that oversees our elections, is legally required to be half Democrat and half Republican. That tells you everything you need to know.
If we're going to change it to make room for additional parties, we have to take over one of the existing parties with an explicit election reform agenda that removes them from the structural landscape and then restructures it (with things like ranked choice voting or a senate that works on proportional party representation) to allow for third parties to gain traction.