I think you've got an admirably optimistic outlook. I hope you're correct. However, I am afraid that you may be underestimating human greed and selfishness. Those aren't unique traits to any generation. Maybe it's human nature, maybe it's learned through existence in a capitalistic / hierarchically organized society. In any case, I am not confident that youth alone will prevent people from seeing the kind of country and world that was left to them, as you put it, and not desire to possess as much of the remnants as possible in an outburst of self-interest.
For every person that sees the ice caps melting and wants to fix it somehow, I'm afraid there's almost certainly at least one other person who thinks, "Hell yeah, new oceanfront property just dropped, how can I own/sell it?"
I'm lucky enough to work for an organization which furnishes me with up to 4 hours of paid leave to vote. Plus, my polling place is on the road home, and I've never waited longer than a couple of minutes to vote. Finally, doing it in person feels more impactful, even if that's just a perception thing.