Learn Dutch: Ik denk dat wij geluk hebben. - I think that we are lucky.

This is because of the word dat (that). It is a subordinating conjunction, meaning it introduces a dependent clause. In Dutch dependent clauses, the conjugated verb (in this case, hebben) gets pushed all the way to the end.

The English translation says "are lucky", so why does the Dutch sentence use hebben (to have)?

In Dutch, you do not say that you "are" lucky. Instead, you use the expression geluk hebben, which literally translates to "to have luck". So the sentence literally means "I think that we have luck."

In English, I can just say "I think we are lucky" without the word "that". Can I leave out dat in Dutch?

No, you cannot. While English often drops the word "that", Dutch strictly requires dat to connect the main sentence (Ik denk) to the dependent clause.

Could I use we instead of wij in this sentence?

Yes, absolutely! wij is the emphasized form, used when you want to put special stress on the fact that we (and maybe not someone else) are lucky. If you don't need that extra emphasis, the unstressed we is perfectly fine.