But he’s not just God. He’s God and Man.
Why didn’t he inherit a fallen human nature like the rest of us, which he would work to overcome?
“how could she be without sin?”
The same way that God made Adam and Eve without sin. Christ kept Mary from sin at her immaculate conception so that she, as his mother, could pass on a perfect human nature, like Adam and Eve had so many years ago.
They weren't "perfect" (God) they were only "innocent" -- like animals are innocent. But since they weren't animals they were capable of disobedience. Animals don't have the free will to disobey, they are confinded to operate only on instinct.