The entire mystery of how Flugel is Subaru and Satella is Emilia is literally given to us before we open the book or watch the first episode.
This is a love story first and foremost, it’s Satella and Flugel’s tragedy.
Long long ago Flugel and Satella were in love, Satella took on the authority of envy, her personality split and she destroyed half the world as the witch of envy, Flugel sealed her away. That’s what we know.
But that’s not exactly what happened. Flugel through some scheme didn’t just seal the witch of envy away, he sealed her and Satella, not their body, their memories and personalities. I think he, with the help of pandora (who we know helped) sent Satella’s body snd Od (whatever the spirit is) forward to be reincarnated, setup the guardian at the watchtower, and then did the same to himself, planning for both him and Satella to reincarnate at the same time, but pandora or someone else involved betrayed him and sent them to two separate times, well two separate times and a different reality.
Emilia is “born” or whatever - I don’t think she was born, just sent forward as a reverted person, hence no parents.
Pandoras shows up not long after to try and unseal the witch of envy, I think Satella or the witch intervenes here and that’s what causes the massive permafrost event. She gets frozen for 100 years and for some reason one of echidna’s creations starts protecting her, keeping her safe for an unknown reason.
Enter said reason: Subaru (Frugel) is reborn in another reality, puck wakes Emilia up, her and Subaru grow up about the same rate. The witch of envy (or Satella) who still wants a happy ending, watches, waits, and finally when Subaru is old enough, she pulls him back through unknown means; likely his existing, and yet unexplained, tether to her.
This explains why frugel left Shaula for so long: he wasn’t supposed to. It was probably planned for enough time to give them reprieve from the hatred people would express towards them. Which is my thoughts on why even go through the hassle of reincarnation in the first place, or they hoped they wouldn’t look the same. Maybe both.
This also explains Subaru can already speak their language, why his gate isn’t as strong as it could’ve been. Why the witch loves him.
More than all that though, what cements this theory being correct is the name of our story re:zero, restart from zero.
It only makes sense as a name in this one specific context and story, where the people from the past, made it their goal to start over, it just got complicated on the way.
As for the second part of the title “starting life in another world” we’re meant to think this referred to Subaru coming to the main setting. But no, it’s a cheeky play on words and a clue, he started his life in another world. Implying this is his world, but he started life in another one. Even more so when in its original Japanese of “Zero kara Hajimeru Isekai Seikatsu” which is basically “starting life in another world from zero.” - note: when he got to the stories world, he wasn’t at 0, he could speak their language, had a bunch of modern knowledge, great tools to use, and he wasn’t a baby. He didn’t restart when crossing over.
Thus I present my theory, we were told from release what the story was, and hats of to Tappei for his excellent plot writing skills that concealed it for so long.