The mission title will have the words Imperial Navy or Naval or similar phraseology in it. And only offered by Empire aligned factions. Also I think you are more likely to be offered it from a local faction that you have a higher rep with (ideally Allied).
This look for a system with msotly Empire aligned factions get to at least cordial and is better if you get to friendly with them and look for mission with "Navy" in the title.
It wont tell you it's for ranking up either so it could be a "navy kill contract" mission or a "navy needs water" mission etc.
Key things is find a system that has lots of empire factions, make sure you are at least cordial but even better be friendly with those emp faction and look at the emp faction mission boards only.
I do believe you will see them more in the non controlling emp faction mission boards.
Use the cred donation missions to get to friendly faster with the emp factions if you are in a hurry and mode flipping helps.
About the be codial thing, if you are "just"
cordial instead of
friendly with a faction sometimes the navy mission will be under the
conditions not met at the very bottom of the mission boards, this can also happen if the navy mission is a cargo run and you are in a ship with no cargo space.
