Zohran Mamdani DSA strategy / Forward Party strategy. Run DSA and Forward party candidates as Democrats in Democratic party primaries. With approval voting or ranked choice or STAR voting, they can win the primary. Then run against the GOP in the general election in a very blue district.
Jesse Ventura and Bernie Sanders strategy. Charismatic populist candidate that people love. Run as a generally likeable independent and have name recognition and a truly populist message.
Justin Amash strategy. Run as a Republican, and then when elected, change party affiliation to Libertarian. Libertarians could potentially run as social libertarians, Georgists, or geolibertarians, as Democrats then, when elected, change their party affiliation to libertarian.
Why change affiliation? They would probably hold more power as Democrats, I would think. But yes winning the primary of a major party is how third parties get elected.
How would Jon Stewart do as a populist democrat?
I don’t think there’s a blanket “optimal strategy” that works for every race. In my state, Washington, candidates may state that they “prefer” some party, but it’s literally just a 18 character free text field that has no effect on electoral mechanics. The decision of whether to run as a democrat is much different in New York, where you have closed primaries.