Since the beta kids knew about their guardian’s session, they were able to figure out where it was and escape to it before the scratch. Do you think it’d be possible for players to escape the scratch and stumble upon a random session if they didn’t know where they were going in paradox space?

Depend on how they escape. I’d assume the easiest way would be through the Furthest Ring, but remember, there’s. Nothing. No landmarks, nothing to guide yourself with in the Furthest Ring. You’d need a Seer of some kind that was able to predict something, to have your Time and/or Space Players to dedicate a chunk of the Session merely to learn about the Furthest Ring, and some means of propelling some sort of ship through literal nothing. If you’re saying stumbling across a random Session? It may happen by mere chance. Or they could spend Millennia in the same location, unmoving, before crashing into a future version of their empty ship. Predicting the Furthest Ring is nigh-impossible. Navigating it for Trolls and Kids was a fluke. And don’t even get me started on the meta of John and Jade escaping by literally breaking the Fourth Wall.