Prevention is the best cure. I know it takes 2 tyre levers to deal with a flat on my road bike, so I carry a pair of decent ones (with some silver paint on them so they show up better by torchlight). In addition I carry a third, old and worn but known good, because I've been known to snap plastic tyre levers (luckily at home). They can also ping off into the middle distance so a spare is no bad thing. I might swap this third one for a metal lever if I can find the ones I've got tucked away somewhere. Even if you could find (hard enough) wood, carving one requires a reasonable knife, which isn't part of a standard bike tool kit, though it is part of mine.
The fallback is other riders. I'm sometimes out solo at all hours hence why I go so well equipped (though rarely to the extent of carrying cutlery) but on many of the rides I do there are other riders on the same route. Some of them are likely to be with or behind me even if most are far in front. Even riding solo there are likely to be other cyclists around during the day.
Any rider can be struggling with a mechanical, and that's why you should slow down and check that a rider standing by the roadside is OK: one day it might be you, and looking after each other is the right thing to do anyway.