It wouldn’t eliminate her from consideration. I’m probably that arrogant (and possibly naive) enough to believe her decision to sleep with me on that first night had everything to do with me. As opposed to her simply being fast.
I had sex with one of my ex’s on the second night (woulda been the first, but there was a mixup) and we had a 2+ year relationship afterwards. I definitely had thoughts of her being the one, but it just didn’t work out. Had nothing to do with the fact that we had sex so early. I have no problem with a woman jumping in the bed early, but if I see that’s a habit, rather than an occasional moment, I may change my mind.
She would still have a chance in my book to call herself the “the one” but it would definitely make me more aware of her actions and interactions with other males. I would have my doubts but would definitely give her a chance to prove me wrong even if she did sleep with me the first night. It could just mean she knows what she wants and men always love a girl that knows what she wants.