Once you meet US ATP requirements, you could get hired at US regionals with King Air time.

For the majors, pretty much no way unless you are very well connected (ie family in senior management). They like internal references, 121, glass, and turbojet experience. 5000+ hours and 121 check airman experience seems to be the ticket these days.

In your shoes (assuming you don't have friends at US majors) a regional would be the fastest path to the majors...you'll have the opportunity to get the kind of experience they look for as well as meet people who may be in a position to provide references later.