I was an SO with only a few thousand turboprop and a few hundred P2X (Which probably counted as NOTHING). I got in, no type rating on 320. Full type rating course was done.
I am sure there are many SOs that had my similar experience plus more! HK Express is also starting their Second Officer program for pilots with less than their First Officer Requirements (1500 TT), the difference is these Second Officers will actually fly! Much better option for cadets who need to gain that experience.