They didn't, not always. Many cultures celebrated, not the solstice, but the day when they could tell that the day was getting longer and thus someday summer would return again.

The solstice wasn't necessarily the shortest day of the year (though it is). To these people, it was the day when the Sun at noon was lowest in the sky. That it was definitely the shortest day seemed likely given what else they knew, but they often could not measure the length of the day.

Measuring the comparative height of the Sun in the sky, however, takes a stick, the ground, something that can mark the ground, and some patience.