And that's exactly right: the only way to get more people of working age to a region without increasing the world population is with migration.
I think its a valid way to solve that problem. In Canada, the STEM programs are filled with 2nd/3rd generation immigrants that were labourers, servers, restaurent workers, etc. These guys/gals go on to get 40-80k salary jobs after uni/college and pay significant taxes WHICH help pay for medical/state pension for the aging populaion
It's not solving any problem[1], and Canada is an extreme example as a country and can't be used as a model for (mostly) monocultural countries.
1: First people argue there's no problem with low birth rate, and then people tell that they're solving the problem. Pick one.