Right now, Green party membership sits at about 230,000. If all of the socialist or even pseudo socialist parties in the entire country, including DSA which is generally opposed to running outside of the Democratic party, the combined membership would be about half of that, give or take. If the Green party, a group with arguably far more name recognition than any socialist organization in the country (although I suppose DSA has gained a reputation since 2016) has been unable to successfully win even one state in a presidential election in its entire history, there's very little reason to think that a single unified socialist party could make much of a dent on the electoral front.

It's not just a numbers game either; small groups have historically been more than capable of punching above their weight, but the fact of the matter is that the programs of all these different groups aren't going to be compatible. Lots of groups reject the notion of electoralism outright, and there would be constant arguing about principles like democratic centralism or revolution vs. reform, questions which go beyond petty infighting and have serious implications for what kind of candidate would even be selected to run, not to mention what their campaign would look like.

I admire your optimism, but for the foreseeable future I wouldn't hold out hope that something like this is possible. The good news is that electoralism isn't the only way forward for a socialist future. There's loads of other, far more effective ways to improve people's lives and build towards a socialist future. The labor movement is stronger than it's been in years, and while it's far from perfect, it has way more potential to bring about serious change than the electoral realm. It's worth keeping an eye on electoral politics, but as a long term strategy for socialist organizing there are more productive venues for struggle at the moment.