Mcbruce is right on and in addition you would need to do a winter operating in the company.
I fear that despite your experence the only way to join right now is via the cadet route into the rhs if your not rated on the 737.
Be aware that there are no guarantees in ryr. I flew with an fo the other day who did what your proposing, good pilot, very experenced on other types in previous companys but 3 years later sadly has not been promoted for this and that etc. This person joined as a captain off a turbo prop.
Good luck!