Married woman working in KSA

I am a married American female and have a family. I am considering a job offer which is supposed to start with 3 months in KSA and then go remote to anywhere in the world.

I do understand the culture but am curious - is it possible for a married woman to work and live in KSA for 3 months without a male guardian or her husband?

Yes, it is possible. Her sponsor will be the company she works for. One of my guitar students was such a case.

Just note the tendency for things here to drag on beyond their forecast dates.

Ofcourse you can stay.