This is the most difficult part, Finding the first job as a fitter to get a foot in the door, I know many people who spent a lot of money to do thier 147 courses hoping to become engineers and eventually ended up either shifting to another industry or jobless and that is why I don't recommend the 147 path to anyone wishing to join this industry at this time, I always recommend the 145 route (aka find a fitter job before doing the modules)because you will be earning money and secure a job, Since you finished your course already and are amid the swamp there is not much that you can do about it now, You should of sought advice before considering to enrol at this program, The only thing I can adviceyou now is make a nice CV and forward it to as many airlines and MROs as possible you may find someone willing to hire unexperienced folks.
The industry is in a huge down turn at the moment and airlines will never bother to develop thier own engineers out of unexperienced folks and rather hire someone who's already experienced, And it's very difficult to get a technician job aswell if you don't fit the experience mould (most airlines typically look for 5 years+ experienced technicians),
Good luck