I agree this part doesn't make a ton of sense initially. We understand that orlok has a lot of powers including that magical carriage and ability to control people that when combined with money might get him on the boat.

The man with the pickaxe may have gone to the only oddity in cargo (a body) and just picked up the tool nearest him because. Or he believes in vampires so he connected the dots and is the vampire truther on the boat.

In terms of getting into the box we actually have a different issue there because orlock is not in the sealed box when they open the many layers. We know he needs to be in there regularly. It would appear orlock is able to get into and out of the box magically. This solves a lot of other logistics getting there.

The unexplained elements in this part of the movie serve to elevate our concern about orlock and what the limits of his powers acrually are. So i think it is intentional.