Its a principled but somewhat brave move to rule yourself out of paying for a type rating because just about most places now do charge cadet entry pilots for a type rating.
Where I work, a significant number of fATPLs got interviews for pilot positions via working within the company doing something else (dispatching, flight planners, cabin crew, crew bus driving, the list goes on) but a significant number didn't pass the interview, leaving them in a tricky position. Those that did get the job still had to pay for the type rating.
I can't think of any "shiny jet" operators (i stand to be corrected) other than BA who are currently recruiting who don't charge their cadets for type ratings.
You may find work in a smaller turboprop outfit via back room work within the company, but there is the whole new issue that the TP drivers seem to be debating at the moment; does career progression from TP to jet still exist?
Maybe you will be happy flying TP for 40 years. Nothing wrong with that, obviously, but it shouldn't be a crime to say you fancy ending up in a B787 or A350.
I would say apply for everything, whether it involves a free TP rating or a paid-for jet rating, and take whatever comes up first. First chances are rare and there is little to gain from narrowing the field.
Best of luck.