Temporary Coverage for Sand Driveway

If it's heavily driven on, it's likely extremely compacted, which only increases the water run-off and retention (since it can't properly drain anywhere).

can you use gravel? A gravel driveway would likely be the easiest solution.

Barring that, you could look at using a grid 'pavement' system:

It lets you plant grass without the turf having to take the brunt of the vehicle weight, so it remains porous.

Concrete is one of the more tricky trades. Ground prep is the #1 important thing. Proper base thickness, and proper compaction are key. #2 is a proper mix; too wet and too much water (typical) weaken the concrete. Instead of fiber mesh, use plasticizers to allow the concrete to run better but without adding too much water. And finally proper finishing can have a pronounced effect in many possible ways (cracking, spalling, blowouts, etc) All these things are much more important than thicker concrete.

On that note, going thicker with the concrete does add strength namely for two reasons: first you can add rebar in the bottom 1/3 of the pad to reliably strengthen it (4" +/- concrete this is very hard to do and does not have the same effect); second it makes the pad be able to handle more ground settling without cracking (given the other conditions are the same).

But an additional 33% more concrete will add significant material cost that would be better spent in other areas first (proper ground prep, proper mix and additives, proper concrete contractor)

As for the fibers, the small microfibers really don't do as much as one might want. Mostly they help with keeping the surface intact over time; they do not help with over all strength of the pad. Macro fibers can add strength to the pad, but mostly due to cracks from expansion and contraction, not from ground settling (from my understanding) and you will see them because the fibers are long.