Some hospitals do use CNAs for NICU, although there are multiple names for an aide position; for example, we use "patient care technician." I would suggest trying to get into a children's hospital as it will probably be easier to move from a pediatric floor to the NICU if you have the peds experience. PCTs in my hospital change diapers, take temperatures, and NG or PO (bottle) feed infants. As well as miscellaneous stuff like picking up blood or running labs downstairs.
When you're a student, see if you can get days in the NICU during your pediatric or OB rotation. Most schools offer a practicum at the end of your course where you spend a quarter or a semester doing a specialty and you can see if you can request NICU (this is what I was able to do). There are various certifications you can get and I would recommend getting NRP (neonatal resuscitation program), although I would try to get it later in your program because it is a bit more difficult to grasp since you'll have little hands-on experience with babies in a code situation. I got it during my senior year of nursing school and I feel like it shows some of your commitment and passion for NICU.
Best of luck, be sure to keep us informed of how things go; be sure to read the threads about how it can be difficult to get a job in the NICU straight off the bat, although the economy may be significantly different in a few years after you graduate. Utilize the search function on this forum liberally and you'll find many answers to your questions because most of them are asked each week.