It kind-of depends on what licence you're going to use to fly. You have a couple of choices.
You can get an FAA Student Pilot Licence which doubles as your FAA Class III medical. As a student, you'll fly under the oversight of your instructor, but the hours will be PIC hours anyway. If your instructor is happy with your night performance, he or she can sign you out to perform night flights. But as a student, you won't be able to carry passengers.
You can get an FAA 61.75 "piggyback" PPL, which is "based on" the validity of your EASA PPL. All limitations of the EASA PPL apply, including the "no night" restriction, which will only be lifted after you get the EASA NQ or IR. It is technically possible to add ratings, such as the IR, to a 61.75 FAA PPL, but as the FAA does not have a concept of "night rating" I don't think that's going to fly (pun intended).
You can also get a standalone FAA PPL. You will obviously need some additional training to get to the five night hours and the number of landings, and maybe some other stuff. Then you need to do the FAA written (which is a single exam) and the FAA skills test. This then gives you an independent FAA PPL to which you can add other stuff such as an IR. And obviously in this PPL the capability to fly VFR at night is implicit.
One thing to watch out for is the medical though. On an FAA 61.75 "piggyback" PPL you can either use the relevant FAA medical (class III) or use the medical associated with the underlying licence - in your case an EASA class II. But for an FAA standalone PPL you need an FAA class III medical, and the same thing applies to your student licence.
Oh, and example one and three most likely require TSA clearance, whereas example two (the FAA "piggyback") does not. It can even be argued that for example one and three you need an M-1 visa.