This is the sentence…
The T-shirts for us will arrive later as for cost saving reasons HQ delivers those by sea. We expect to arrive first to Hungary within 4-5 weeks.
and this is how I understand to use of the word expect
We expect to arrive means that somebody thinks that we arrive within 4-5 weeks
We expect them to arrive would mean that we thinks that the shirts will arrive within 4-5 weeks
What do you think?