I'm from PA so my experiences may not translate exactly, but here's what I have learned in a tough job market (Philly metro area). Get a job as an NA/PCA/whatever on a floor with an acuity level you may want to work with. Even working two days a week is a good resume builder. Just show that you are committed to healthcare even prior to graduating.
Find an area of healthcare covered by the new grad program you want to apply to and be passionate about it. I knew towards the end of nursing school
that my passion was emergency medicine. I thought long and hard about what
I loved about the ED, and how I could best sell myself to the nurse manager during an interview. Figure out what you really love, and when you get your face-to-face interview let your excitement and passion shine. A LOT of employers are willing to overlook an experience deficit if you showcase a passion for your specialty and and eagerness to learn everything you possibly can.
Have an excellent resume that details WHAT you have done in clincals, how much and for how long. As a new grad your clinical experience is all you have to go on, so use your resume to highlight that. Even if it bumps your resume to two pages. I was always taught a "good" resume should be concise and fit on one page. However, I've found that if you're applying for a specific professional position it's OK to bump that to two pages in order to highlight all of your experience. Don't be afraid to break that two-page barrier if it helps you sell your skills and experience.
Finally, APPLY EARLY. I missed out on a few really excellent new grad programs because I applied too late in their cycle to be considered. Even if you don't have your degree or all your paperwork together, APPLY. Attach a note explaining your circumstances and how you would be glad to provide additional documentation as it becomes available. Call HR (if they allow that sort of thing and have a number available -- some have gome completely online and make contact info impossible to find) and explain your application.
Really my tl;dr best advice is to find what you love about nursing and pursue it. Let your excitement and passion carry you, but back it up with a strong resume, work experience and faculty recommendations if you can get them. This is what worked for me, so I would happily recommend it to any new grad looking for a leg up.