There's been a hint already that baby Elsa isn't acting like she would be if the time travel didn't happen, with that scene of her looking out the window saying "it feels like someone's calling my name". She also cast that eye gouging spell and for Evie the only reason she was using real magic at this age was due to her future memories of education coming back in time with her.
I think we can safely assume on the timeline portrayed in the game, Elsa did not pick a fight with the slaver and lived for them all to make it to the orphanage some other way. This Elsa we're seeing is externally influenced in some way that breaks from that plot.
It's also possible that if Yvonne hadn't gone back in time to save her in this moment, one of the other love interests would have instead. Or, alternately, it's possible that if Evie didn't come by, someone else would have intervened.
Either way, it's not really worth fussing over.