To explain seasons you do not need a precise measurement of the inclination of the ecliptic, it is sufficient to know the fact. I suppose that this fact was known to the first people who started agriculture, that is more than 12 thousand years ago.
Indeed, agriculture strongly depends on the change of seasons. You have to know when to plant your plants for optimal results. 12 millennia ago, people did not have calendars (not speaking of internet), and did not even know the precise length of
the year, and they did not count days (from which day will you begin your count anyway?). So how did they determine when seasons begin and end, and when
it is appropriate to do seasonal agricultural works by observing the sky?
Only by astronomical observations.
It is clear that you will get poor results if you rely on "today's weather" for
This is confirmed by the earliest texts on agriculture that we possess, like Hesiod. He does not write "On March 27 do this and this" but he writes
"When Sun is in such and such position on the sky (with respect to such and such star, do this and this".
We do not know whether peasants did astronomical observations individually or were advised by
their rulers or priests, perhaps the practice varied from one culture to another.
The beginnings of the seasons are determined by simple astronomical events:
equinoxes and solstices. So any ancient agricultural society must have been aware of these events, and on the motion of the Sun on the ecliptic.
Position of the ecliptic in the sky determines that the days are longer and the Sun
is higher in summer than in winter. So what can be more natural than to assume
that this is exactly what CAUSES summer and winter? It is clear that we obtain all heat from the Sun (I am not counting firewood). Thus the warm season happens
when the Sun stays higher and the days are longer.
And this inequality happens exactly because the ecliptic is inclined under certain angle.
Of course we do not have written sources from 12 millennia ago to confirm all this, but it seems very plausible that people observing the sky were aware
about connection between seasons and inclination of the ecliptic, since these observations began, that is since the beginning of agriculture, the latest.
And the earliest known manual for agriculture (Hesiod) confirms this.