Firstly, "core" and "original" are not terms used in the clinical side of things. There is no such thing, as there was never one full personality in your body. (A good analogy is a dropping a pot and it shattering. Which piece is the original? None, they all come from the same pot.)
I have been the host for most of the life. I don't have memories of a lot of childhood before the age of 8. I've often wondered if our host was different then. Who knows! I don't. I wasn't aware of any alters until I turned 22. I heard voices sometimes and had a lot of amnesia and out of body experiences but I didn't really understand it as DID. Just thought I was crazy.
And hosts can be a different gender from the body, that's not uncommon. Before I knew about the system the co-host was our gatekeeper, a cis male named James. We co-conned a lot. I didn't know it. I was certain I was transgender because I felt male ALL THE TIME. It was just his feelings of being alienated from the female body. He still feels a lot of dysphoria every time he fronts. Not just on the male aspects, but also on size. Inner world he's like 6'7". I'm 5'5". He has huge hands and mine are small. He feels like he's operating a tiny body and it really fucks him up. Whenever we're co-conning I feel that dysphoria from him.
Not trying to say you're not trans, but you could definitely just be a male alter in a female body. You could have been made host in childhood because the first host couldn't handle life. You retained the male gender. If you have a gatekeeper, they can manipulate memories and make you forget stuff easily. (e.g. me forgetting I had a suicide attempt in 2016. I kept remembering it and forgetting it over and over. He was purposely keeping this memory from me, thus forcing me to forget it every time I remembered it.) In our system, I think there was a different alter that was host when I was a child. I was hyper femme, loved girly stuff, etc. But right when my memory "starts" (around 8-9 yrs old) everything about me changed. I became me, as in Jules. My entire family has noted this change. I am non-binary and lean more masc. I have completely different likes/dislikes as the first host. I actually recently met who I think was the first host, almost a year after finding out I had DID.
Also, gatekeepers are very good at remaining behind the scenes. I have a system friend irl that has several gatekeepers. Nine, actually. But she has only met three. She has literally never heard, seen, or felt the others, but other alters have told her they're there. They are in charge of different alters, aspects of life, etc. DID is an incredibly covert disorder and it's extremely common for hosts to be completely out of the loop. I was. I didn't show up until around 8-9 and I seriously thought this whole life was mine and mine alone. That's not the case at all.
If you have questions, shoot me a message!
-Jules