Yup, in europe it's pretty common to go from your Frozen ATPL Check directly into a jet type rating for a 737 or a scarebus. Major Airlines like Lufthansa sometimes take pilots direct from flying school onto types like A300s as well.
My current employer hired quite a few pilots who were still in flying school this year just because he was desperate to fill the seats on all those new shiny airplanes, they dont have to pay a type rating as well, just a reduced payscale for the first year (yes, thats paying for it too, just not straight outta your own pocket). It's common practice as well to upgrade them to the left seat after 3000 total time which can include everything thats flying and only 2000 hours experience on jets. Seems to work so far, no major incidents...