One that doesn’t take corporate donations would be start.

Another method is 3rd parties forming locally as grassroots organizations and then forming a coalition party to back 3rd party candidates on the national level.

Sort of how you have a few caucuses in the Democratic Party like the Farm-Labor Part in Minnesota, or Independents who caucus with the Democrats like Bernie who could be peeled off to back a 3rd party of even just flatly Independent candidates.