Continuity questions

I have so many questions about the whole Peter thing in the beginning of season 4. There are so many continuity errors. This is where the spoilers start so if you’re not this far in yet, I suggest you scroll. In the very end of season 3, Peter uses the machine and then disappears. It’s said by the observers that he never existed in these worlds. So the question is: how did they discover another universe? It makes sense that Walter would still be looking into the alternate universe to try to find the cure for Peter, but if he never existed on our side, then that would mean that either Walter went into the alternate universe to try and save Peter and he drowned at the bottom of the lake, or he didn’t go into the alternate universe. And if he didn’t go into the alternate universe, then he wouldn’t have started the destruction in Walternates world, so there would be no need for any other alternate travel. And if he didn’t go into the other world, why are there shapeshifters in our world? On top of all of this, all of season 3 wouldn’t have happened no matter which of these is true if Peter never existed BECAUSE Peter wouldn’t have found out that Walter kidnapped him which means he wouldn’t have run away. If he didn’t run away, Walternate and Newton wouldn’t found him because he didn’t exist so he never would’ve gone to the alternate universe, Olivia wouldn’t have gone back to save him, and Fauxlivia wouldn’t have switched with Olivia since they wouldn’t know about each other, so then the bridge and everything leading up to it would never happen. I’m only on the first episode of season 4 right now, and I watched the whole series about 4 years ago but I forget if they explains it.