From what I've read, cross beak deformities often don't show up until the birds are 6 weeks old or older, and those that are apparent before then are often very severe. In all of the information I've seen, it doesn't seem that there is a clear picture of what causes this. Some evidence points to genetics, some indicates it may be a problem with temp and/or humidity during incubation, and then there's always the chance that it can be caused by a trauma. Either way, it seems that the vast majority of cross beaks do get worse over time.
I discovered one of my EE chicks had one at just 5 days old. It was definitely normal when I opened the shipping box, and when I did notice it at 5 days it was such a slight misalignment that it was hardly even noticeable. Just a very small amount of gentle pressure was all it took to move the lower beak back in line with the upper beak. It has gotten so much worse that her upper beak and lower beak don't even come close to lining up anymore and we've had to trim it to help her better get food in. In fact, if you look at her head on, it seems like her whole face is just a bit crooked, not just the lower beak (which is a lot crooked). She eats ok, she just can't pick things up but can eat really well from a deep dish.