This is entirely up to "we the people" actually.
If we leave it up to our "Western" governments - the likelihood of a HEALTHY rebound is minuscule and certainly not without heavy concessions and BIG losses to the population at large.
But if we stop rolling over for them and demand FULL accountability, return to constitutional values, return to competitive currency, personal and economic freedoms - well, then there's a good chance.
For that to happen, the whole system would have to change. And that ain't very likely.
But your question actually is: will the "non-first-world" countries take the opportunity and zoom ahead?
If their governments had any sense, they'd all follow the few proven near-free market models that exist or have existed. And then they'd surpass the West in a blink of an eye.
But people the world over are just not sufficiently awake or educated for this to happen. As for those that are - they follow the false god of collectivism which is guaranteed to only make things worse for EVERYONE, including them.
On top of that, the failing Western governments would sooner die than allow these other countries to achieve too much happiness.
Will "we the people" ever act to stop our thieving governments?
Sadly, I don't think this will happen in my lifetime.