Unfortunately it's largely a numbers game.
If possible, be willing to relocate for work. Most entry level seekers are applying to everything they can, all over the place.
Work any and all connections you have. Anything you can do to get past the HR filter will help 10x your chances.
If you are pinched for money, you can always look for temp to hire work. It's unstable and the pay is usually crap, but it will get you in the door at one or multiple places and will get you to broaden your network.
Keep at it. It's discouraging and terrible, and the process is largely broken, but its entirely possible.