Your best bet would be to look into charter. Maybe try to snag a street captain gig in Citations or something. Charter turnover tends to be higher as well, so even if you hire in as an SIC, upgrade potential is greater.
As Gauley said, most established corporates don't roll that way. You might be able to walk into a PIC position, but trying to calculate upgrade times from an SIC position is a nebulous undertaking - so many things can change in a department. Not only that, but frankly, if your not cutting it and/or they don't like you or feel you are ready, you're not going to get upgraded automatically, even if the opportunity does come. More factors play into this than just flying skills. You are not a number as in the airlines, you are a team component. If that component is not working, it gets changed or set aside.
Wish we could be more helpful.