Most of the Asia hires EXPERIENCED TYPE RATED CAPTAINS. Few airlines hire FOs but will not upgrade. Emirates, Qatar, Etihad, Fly Dubai, Eva all hire FOs without type rating and time in type but one needs a few thousand hours on jets. Each company has their own other sets of qualifiers on top.
COPA in Panama hires FOs into 737 without time and type. As far as Asia, that is for some seasoned pilots with some few thousand hours.
Like couple of people said earlier, stay in the US if the upgrade is in near sight. Nothing compares to home.