Getting that first full time commercial job is probably the hardest thing that any new CPL will do in his/her formative years.
It seems that you do it two ways : Obtain an Instructing ticket and hopefully a job with the school that issued it or else go and get a charter job, and that is with a new CPL, minimum time - minimum time to meet insurance requirements and enough time on type C172/182/RG/206/207/210 to keep the charter firm happy. (quote: How do you get a job without experience, how do you get experience without a job?).
I started out by having some tailwheel time on the aircraft that was being operated by a charter firm. When I got my CPL They simply said that now that I had a CPL I had better do some part time commercial work with them. I did and that went onto the CV.
I used that entry on my CV to advantage when I chased my next part time job and eventually got a full time job by sheer persistance of calling in and contacting a particular operator, and that was before I even had experience on his type of single engined aircraft.
That first full time charter job (S/E) was then used as CV material to obtain the next full time position.
Look at it from the employers point of view : If he takes on a new CPL he has to keep an eye on him/her for the first 50/100 hours to ensure that they fly the aircraft the way the firm wants it done, that the paperwork is done correctly, that departure and arrival times are met and that the CPL is able to make command decision - in the air and on the ground. All of that can mean a lot of looking over the shoulder of the new pilot until the boss is happy the new pilot is starting to perform without supervision.
All of this means that the more experience the new start has means less superbision he has to put in.