I think you should be fine if that is only the first sanding and there are 4 more to go. The parts that are not stained look beautiful so hopefully it will all turn out fine. Is this white or red oak?

Those deep dark ones do not look to me like anything will take them out.

Go dark or replace the flooring.

In your professional option would you scrap the refinish job and replace the entire floor? I wanted to keep the original floors to the house for histories sake. Maybe the stains will grow on me lol.