I've been trying to write a story for a few years now, and I need some advice.

For context this is part of another persons story so I am limited to some of their rules for how my character gets to Equestria as well as how the story starts.

The basic premise for the story (both mine and the other person who ahs like 45 chapters by now) is this. "The end of the world has come and chaos reigns. those who survived and were peaceful were given a gift by God as this was a test. They can either choose to earth with no memory of that day as the event that caused the end wouldn't happen. or choose powers and a new world."

So my problem is should I skip this part until I've developed some background for the Main Character or just go with the setup and develop them as I go?

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You can always come back and fix stuff later.
My advice is to bullshit your way through the difficult sections and maybe something that happens later will help you fill in the pieces.
Overall, just start writing. Some problems and/or developments won't be apparent until you do.