Zem zem well is not a permanent well.
i don;t get that., what is a permanent well? well there water is coming from a hole., and it is well known since the time of that Abbasid Caliphate 714 AD... And it is serving visitors since that time at least... that is ~1300 years...... i would consider that as permanent., I do not see any reason not to extend that time down to say 100 AD.,
Your map is a fake map : nobody knows Mecca before 700.
I agree that Mecca.... Islamic Mecca,,,,, Muhammad's Town Mecca is fictional story.,...but that is nothing to do with a water hole serving travelers, nomads and animals and what ever since ancient times., OR DO YOU DISPUTE THE EXISTENCE OF THAT WATER HOLE SINCE THE TIME OF ABBASID CALIPHATE?
As far as that map is concerned it is possible it is fake. but we must realize there were kingdoms in Yemen /southern Arabia since ages
., Architectural structures are still there as proof of these kingdoms ;; So there is no reason for people not to travel from Yemen to Israel or Damascus through a coastal route of red sea say from this picture
So just using common sense., i am saying that a possibility exists that zam zam water well is serving travelers since ages .... much before Islam...