Ancient peoples mapped the sky. Being able to track the movement of constellations across the sky, and the height the sun would reach were key markers of when to plant, when to harvest, when the rains would come, etc in times before watches and calendars.

Going back further cavemen would use the stars to know when animal herds would return and when spring was upon them etc.

Constellations were an easy way for them to remember groups of stars, and oral traditions were used to pass stories of said constellations and that knowledge to the next generation.

So long as you figure out that the Sun rises to different heights during the year, you can figure out that the Sun reaches it's height on the Solstice, then you can count the number of days till that happens again.

The reason there's 360 degrees in a circle is because the Babylonians used circles to track the sun year round and assumed (incorrectly) that there were 360 days in a year because it was a nice round number.

It took centuries for people to realize that calendars were faulty and corrected them by adding extra days.