First author researcher on a manuscript left job without publishing

If the slightly outdated paper comes back from review with a decent amount of edits to be made, potentially new portions of analysis, while the first author states that they do not have time to work on the old manuscript, can one of the co-authors potentially take over as first author?

Potentially, yes. Far from a guarantee. Probably the old first author would become second or co-first, depending on norms in your field.

Does the original first author have to give consent?

Yes. In fact, everyone has to agree to the new order, even if their relative position is unchanged.

You need the permission of every author to publish something. If someone withdraws before publication and doesn't continue contributing, you still need their permission. The order of authors also needs to be agreed upon within the set of authors.

I suggest that you get preliminary permission to continue and to submit and then deal with issues as the arise when they arise, not assuming that there will be problems. The rest of you may need to leave the author order unchanged even though the "first" no longer participates.

In my opinion "effort" is a poor measure. Who contributes key ideas is much better and that may already be set. If someone works 12 hours a day and another works five, it is pretty hard to say that the one with more hours has contributed more to ideas. But your mileage may differ.