Everything depends on your profile, and supply and demand. If there are enough NICU nurses with the requisite experience who are willing to go to that location for the underlying bill rate offered, then you don't have a shot. If you find good recruiters, you will be able to get good intel on which assignments you might have a shot at.
A lot of time, requirements are just boilerplate and the right candidate doesn't have to meet them. You are dead right that every unit will want the most qualified and experienced traveler, but their actual acuity needs don't really require that. But they want who they want. You should be aware that will be at the bottom of any pile of traveler candidates submitted (not even prior travel experience and a dead minimum of experience, and if you get a travel assignment offer, you will have to scrutinize it carefully. There is some reason they could not get anyone better. It could be as benign as location or pay. Or a hellhole no one else with a good recruiter who tells it to them straight is willing to work even for higher than usual pay.
I don't know where you are looking at available assignments online but be aware most of the job board ones, and on many agency sites, are bogus "representative" assignments. Tough work to keep everything current, and besides the point anyway for a new traveler. Until you have submitted sufficient documentation to an agency, which usually takes some time, that "assignment" even if real, will be gone.
The best thing you can do right now is get two full years in your specialty in a staff position. Then you will be both more competent and competitive as a first time traveler. After that, forget about agency requirements or agency brands. Just call lots of agencies and pick 3 to 5 with recruiters you communicate well with. No shot of negotiating anything with someone you dislike, or suspect is not being straight with you (you will learn a lot after you have talked to say 15 recruiters), or with whom you cannot communicate with comfortably in your own style.
Then, your goal for your first assignment is not to make big bucks or to go to Hawaii. It is to have a successful completed assignment on your work history, one well within your current skills at a traveler friendly assignment. You improve your odds of that happening by not only knowing that is your goal, but having good recruiters who also prioritize that goal. After that, you can seek more clinically challenging assignments, better pay and locations.