You'll probably have to try a smaller company. They're referred to as "creek outfits" but they will take a chance on an employee with a basic Z-card before the bigger ones will.
They don't pay as well and the amount of steady work can get slim now and again, but these are the door into the larger side of the industry, allowing a person to come in from the street and start building the sea time and experience needed for a strong resume’.
If you have no endorsements but you have your STCW certificate, you may be in better shape than most with no endorsements. Go to the Dispatcher's page and try to talk to some of the companies you find there.
If you don't know what an STCW is, then you don't have one. So go here.
Use the message boards for more advice.