This is most definitely not normal -- in fact, it is so not normal that it is almost surely not the fault of the mattress, which is good news because it could be an easily fixable problem. For it to sag after just one night, my best guess would be that you do not have the proper "center support" in your bed frame. Check under your bed and see what the frame looks like (not the box spring / foundation, but the metal frame under that). If you are sleeping on a queen or a king mattress, it should have the usual rails at the head, foot and sides with a leg in each corner plus a center rail that has at least one leg if not 2 or 3 legs holding up the middle of the mattress (where most of the weight is while you're sleeping).

Even on the off chance that this is caused by a manufacturing defect that is so severe as to sag on the first night, you'll probably need to have a proper bed frame as described above in order to make a warranty claim, since most warranties require that a queen or king sized mattress be used on a frame with center support.

Another possible explanation would be some sort of problem with your foundation (aka, box spring). If it's a new foundation, it could be defective. If it's an old foundation, it could just be worn out.

All that said, the bed frame would be the first place I'd look.