'Born' is the well established canon kiin. Bethesda does not provide any sort of numbers, cardinal or ordinal, so the only 'first' is the fanmade diist. You might find the word kulaan useful - it officially means 'prince' but could be expanded so as to mean 'heir' or 'successor to the throne'.

"First born" has a connotation that's dependent on the culture of the language it comes in.  First born just so happens to be important when it comes to inheritance.  For your language, you should take this into account when creating your words.  Do you have canon associated with your language?

For Dovahzul, Odahviing states that Alduin is "du'ul zeymah" (crown brother).  This could be the closest you get to the concept of first born.

Therefore, "first born" in this case is "du'ul kul"