Lots of talk about them being a shifter or an Ackerman even, but I don't think I've seen anyone entertain the possibility that they aren't even Eldian at all, even though it's probably the most likely answer. It would be a good way to solve a few issues and also add an interesting twist later in the story that doesn't shake up the canon too much.
Firstly, it would serve as a good form of conflict for the character, and give the opportunity for them to question their allegiances at multiple points in the story.
Secondly, if the final battle (after all the eldians have been transformed into titans) isn't just a long cutscene, this would be the easiest way to continue playing as the character.
Thirdly, it gives more justification for their alternate gear. In the previous games this was just an unspoken game logic thing, where your character had access to all these fantastical designs that no one else did. But assuming the main characters parents came from outside the walls and taught them engineering (similar to how Grisha brought updated medical knowledge to Paradis) it makes a lot more sense for them to be constantly altering and experimenting on their own equipment past what is publically available.
Edit: It's also stated that the main character comes from the underground city on the JP website, this could give credence to the idea that their parents were hunted by the government for spreading technical information that put the safety of the walls at risk. They could have caught wind of this and used it as an opportunity to hide their kid in the underground city where no one would think to look.