TL;DR It’s correct to do so.

You’re right to identify s’ as another way that French could have fixed the vowel + vowel problem (hiatus), but the apostrophe strategy is reserved for very few words.

Much more common is the liaison strategy, where a consonant turns up. Usually that’s done by pronouncing the otherwise silent last consonant of a word, as in "les arbres".

Other times it’s done by inserting a consonant out of nowhere, as in "Sera-t-il ?"

And in this case, we have the very interesting solution of switching to the masculine possessive, which has that convenient consonant n on the end!

Notice that if something else comes between them to fix the hiatus, we see the feminine as expected:

Voici mon école.

Voici ma belle école.

If there’s something else but it doesn’t fix the hiatus, then we still need mon.

Voici mon excellente école.

P.S. If someone knows the etymology to this, I’d love to see it. As far as I can tell from the TLFi entry, sa is how the feminine possessive always looked. (Whereas if it originally looked more like son, then we could have wondered if instead of "switching to" the masculine, an older form was just retained.)