That is not accurate: to first approximation, growth *creates* capital
some explanation ...
If productivity rises, firms and individual create a larger surplus that they can then deploy as capital, or investment, for even greater output.
This is the bottom line to keep in mind
Not really
Almost always, the constraints societies face have to do with organization, management, trust, rule of law, experimentation, institutions, innovation etc.
Consider a country that is currently producing 50 cents per inch of land when its neighbor is producing 1$
so once you improve on these margins and earn the extra 2 cents per inch and so on ...
this is the virtuous cycle that we call growth - especially for poor countries
poor countries don't need to beg the rich - they have within them everything they need