I'm not a doctor so I certainly can't asses your problem but I also had lower back problems when I started biking again after a long time off. It was, as you said, just soreness from not having used those muscles in a while. Cycling is pretty intensive on your back, so it may just be that. It may also be your bike fit as others have noted.
Another common cause of cycling related back pain is lack of flexibility, particularly in your hamstrings. Can you bend over straight legged and touch your toes? If not, start by stretching your hamstrings every day for a few weeks and see if that helps your back pain.