Progressives need to co-opt the Democratic Party the same way the Tea Party and MAGA took over the GOP. Build a base, win primaries, and force the establishment to move left or get out of the way.
You're missing a pretty massive step one there, which is "Get your party bankrolled by wealthy oligarchs in the U.S. and Russia." The Tea Party would not have seen any success if it wasn't for the generous contributions of the Koch Brothers et al.
There are groups working to do that. We don't have to talk about this as a hypothetical can get involved today
For instance, groups like Indivisible are pushing for Schumer to be pushed out. Groups like Run for Something are supporting progressives under 40 to run for all positions in state and local elections (generals and primaries)
Say, for example, someone started a "Socialist" party. Running mainly on domestic issues such as worker's rights, proportional taxation, rescinding the idea that corporations are people in the eyes of the law. But WITHOUT a clear stance on culture war baggage such as trans rights, DEI related talking points and "wokeness". Those would be considered state issues and not a domain for the federal government since it distracts from actual geopolitical issues such as wars and climate change catastrophe mitigation.
Would anyone be interested in that? Basically a party that focuses on issues in a similar way AOC does. Socialist, but not communist as I consider the US constitution and the right of elections untouchable. Liberal-socialist, in a way.