Break out from national champion to global champion - WM Investment Research

I have recently started (I am relatively fresh out of uni) on an Investment Research position in Wealth Management (investment strategy dep.) with a firm that is very well regarded in my country, and our region of Europe in general. They are however not so very global. I could be very satisfied with my career here, as I am working with the things that I really enjoy working with, at a scale that is not too shabby all things considered. I have however thought about if I'd might want to do some years abroad at some point in my career, specifically for a global top firm in the same field.

My question is regarding the how difficult it would be for me to, in a few years, go from this national champion to one of the global champions (e.g. Vanguard, Blackrock, State Street or something like that), within the same business function, i.e. investment strategy/portfolio management. Also, would there be any steps that I should take early on to improve my chances down the line, as for example, should I take a CFA or CAIA within the next two/three years or so, before going after such ambitions.