I suggest it from the presumption that you'll be looking to build a worker and farm as soon as possible.Notice that Agriculture was researched on turn 30, but as of turn 55 there are still no farms.
I ran some tests using fairly similar build/tech patterns. I found Agriculture -> Animal Husbandry -> Pottery as possibly the best tech path. Delaying Hunting seemed to produce the best results. Prioritizing Hunting resulted in the most worker turns spent on road building (rather than actual improvement building).
Outside of substituting a scout for a warrior, I don't see how you even intend to leverage Hunting before starting on your first settler. While the settler builds, you have time to research Archery in any of the configurations I tested.
For what it's worth, given the free Fishing, Agriculture -> Hunting -> Animal Husbandry -> Pottery wasn't even that far behind the two shorter tech paths. It started its first cottage 5-7 turns behind the other two paths, but reached size 4 before starting on a settler.