Are you an active member of your local Democratic party? That’s the best way to get leverage over who your state party’s nominees are. Congress elections are every 2 years, so really a pretty narrow window.
You can also find critical elections and try to help the candidates. In 2005 I saw that Melissa Bean had a chance of ousting Phil Crane in the Illinois 8th district. I had some skin in that election, as when Crane first ran (in what was then the 13th district) in 1970 I was working for his opponent; we ran a weak, underfunded campaign that we should have won, and Crane was subsequently one of the worst people in the House for decades. For a variety of reasons I didn’t much like Bean (who incidentally went to the same high school as HRC), but I saw that she had a chance of beating Crane, so that year I gave all the money I usually divvy out to candidates to Bean. She squeaked past Crane, whose political career never recovered.