I can tell you there are a lot of mariners out of Jax looking for work right now. Not to be gloomy but you should know that's what you're up against. As you probably know very well, the slowdown of OSV work in GOM means there a lot of competition for jobs close to home. That being said don't stop looking. It may mean you will need to look for work farther afield. I looked for my first job during a maritime-job depression in the 1980's and found work in a week, all the while listening to my friends complain there were no jobs. What I found out was that there were no jobs where your hands stayed clean. Different thing altogether.
As other commentators have mentioned, it's mostly a matter of shoe leather, made easier by some research on the Web. Many knowledgeable people have posted elsewhere in these forums about making the circuit of the OSV companies. I won't repeat what they have said; take the time to research their posts. There were some good ideas just a few posts before this.
A source of first jobs in the industry, at least in the past, was to get a job on oil spill recovery vessels. These are vessels that are tied up to the dock most of the year, waiting for an oil spill to occur. Not a lot of underway time, not a lot of money (though I may be wrong in that) but the jobs seem to turnover relatively frequently for whatever reason. Perhaps someone with experience on those boats can set me straight if I am wrong in that impression. You can find these boats around most of the major ports. MSRC is, I believe, the largest operator. Again, with the downturn in GOM these jobs may be taken, but the country does have two other coasts.
Where I work, in the Pacific Northwest/Alaska region, things are slowing down till the end of the year. Fishing vessels, processing vessels, freighters, and tugs will be busy until the end of August. Then the summer rush is over and only the "steady" people with each company will see work in Fall. You will see some relief work around the holidays, then with the first of the year hiring begins again around here. Fall is the slow period in PNW/A.
Don't listen to people who say there are no jobs out there. For the most part there are simply jobs that other people don't want to do. If you walk around enough (and it may mean travel) you'll find work. If you're green, young and have good work ethic you won't turn your nose up at jobs that will get your hands dirty and give you a sore back, if you truly want experience. You may find that you'll actually like them. Stranger things have happened. If you 're older and have changed careers remember what you should already know: you have to start from the bottom like everyone else.
Good luck to you.