I won't start working in the NICU until another couple of weeks, but I can answer the ADN question and stuff from what I know about my hospital. I also have my ADN. I am an experienced nurse(not by many years, almost 3), but I am finishing my bachelor's currently. My NICU hires new grad ADNs. My whole hospital does. Our NICU is a level 3 with ECMO, surgeries, nitric, total body cooling, etc. My hospital is a teaching hospital and a level 1 trauma center. I think whether or not the NICU you want to work in accepts ADNs will vary from area-to-area. I have heard of other hospitals in my state who will not hire an ADN RN, even with years of experience, unless they are currently in an RN-to-BSN program. So, I would just do research before you apply, but it is definitely possible if that's what you want to do!
As for getting a "foot in the door", there are ways. Some NICUs allow volunteers to help feed and rock babies who are stable enough. The NICU I will be going into does not. Some also use techs. The NICU I'm going into has a few, but there is not always a tech there every shift. Something you can do if you have your heart set on a certain NICU that doesn't allow either of those positions is to contact the manager and just let him/her know how interested you are in working in the NICU after graduation. Maybe you could ask for a shadow day. A lot of managers like that(if it's allowed at that hospital/unit) because it lets them know that the person has actually seen a day or two(or as often as you can) in the unit and they still want the position after they know what happens on a typical day. The NICU is a good area for this because not all nursing schools do a NICU rotation, and people want NICU because they "like babies" a lot of times. The manager I'm going to has you shadow because she's had high turnover because of that in the past. People want it because they love babies, but are shocked to find out what the NICU is really all about and what states those babies are actually in.
Sorry this is so long, but I think there are definitely ways to get yourself noticed and get there with only an ADN! If your nursing school does do a rotation in the NICU, or even just in OB, you could maybe ask your clinical instructor for any tips or if she/he knows the manager and could arrange for you to meet!
ETA- Even if your local NICU doesn't allow volunteers or CNAs, you could try for the wellbaby nursery. Any kind of experience in a relatable area will look good and help you network by getting to know others!