Can I ask to be the first co-author?
Yes, of course you can ask. But in some fields there are other considerations that are considered important and first authorship is assigned for reasons not obvious to people from other fields. Sometimes those reasons are just political, but people go along with them to keep peace. It might also be necessary to keep the peace with a supervisor who has authority over you and can affect your career. 

So ask, even if you might not get what you think is fair. Think long term and preserve relationships. Having a publication, even if not as first author, is still valuable. 

And there may be future work that you can extract from the project that won't bump up against the same considerations, making your own first authorship the obvious choice.