We kind of saw this in Age of Calamity, but that also allowed them to get control of the Divine Beasts. If they were able to escape, Zelda still would have been able to seal Ganon and the Divine Beasts would have been powered down.
Thus, Urbosa would go back to leading her people, and potentially have kids. This would mean that, while Urbosa would be dead, Riju wouldn't be the chief by the time Link woke up, one who was possibly more competent than Riju and would have prevented the Thunder Helm from being stolen from Gerudo Town.
Revali would have returned to Rito Village, and I would suspect a decent amount of Rito nationalism to take hold (I'm actually surprised that there wasn't as much Rito nationalism in the present day, I would have expected it to be more like the Zora). Kaneli would still be in charge of the village, but there would be a much more skilled Rito army as Revali could have taught his techniques to the Rito.
Mipha would be alive and well, which would have probably led to the Zora having less nationalism. The Zora could have helped the Hylians rebuild Hateno or flesh out the Akkala region, something they likely didn't do because elders like Seggo and Muzu were so distraught at Mipha's death. It is also highly likely that Mipha and Link would have married in the present day.
Daruk would have returned to Goron City. I'm not sure if much would be different, Bludo probably would have founded the Goron Mining Company and their society would have been pretty much the same. Daruk would have gotten to meet Yunobo in person before dying.