I suppose we should make a few tests to be thorough. Fill the world with religious focused leaders leading civilizations without mysticism and see when Buddhism and Hinduism are founded.
Man...I am going to lose the challenger series...SGOTM...obsession!

I am going to make tests right now and then put it in this post.
DanF provided us zealots, then shall be the opposing leaders and I will take away all their knowledge of Gods.
If we need to found Hindu in Delhi then moving northwards (on the Stone?) for a central shrine would be preferable, since the chance of auto spread decreases with distance from the shrine.
Ha! Stone settling is good after all. I mentioned about centralizing the cap earlier.

Just kidding.
As we are forced into the early religion, we might as well make the most of it ... thus the early GP. Due to the Philo trait, the GS for an academy won't come that many turns later, right?
You are right about it, but (always one), when 1000 GPP reached, we make a jump, thus less GPs, decreased rate until 3000 GP.
If we are gunning culture, better be careful with what we wish for.
If we are going for a large war campaign, we might save many GScientists for Astro and maybe Engineering given we don't have fishing.
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Quite frustrating. Regenerate a map means all tech changes are lost.
But I can't use the same map and new random seed, we need many maps to pinipoint true variability.
I use different maps and new random seed. I know some types of values are retained with regenerate map like personalities in random personalities...
List:
*According to the new rule, all dates hereunder are the reported dates, not the actual founding dates by the AI, which happened the earlier turn*
Test #1 :
Buddism ==> T15 - 3400 BC
Hinduism ==> T17 - 3320 BC
Test #2 :
Buddism ==> T14 - 3440 BC
Hinduism ==> T17 - 3320 BC
Test #3 :
Buddism ==> T15 - 3400 BC
Hinduism ==> T16 - 3360 BC
Test #4 :
Buddism ==> T13 - 3480 BC (Zara had an oasis tile in first culture ring)
Hinduism ==> T19 - 3240 BC
Test #5 :
Buddism ==> T13 - 3480 BC (New map with Zara and first ring oasis )
Hinduism ==> T17 - 3320 BC
Test #6 :
Buddism ==> T15 - 3400 BC (Izzy)
Hinduism ==> T22 - 3120 BC (Mansa)
Test #7 :
Buddism ==> T14 - 3440 BC (Mansa)
Hinduism ==> T22 - 3120 BC (Hatty)
Test #8 :
Buddism ==> T13 - 3480 BC [Izzy with double oasis in first culture ring o_O]
Hinduism ==> T17 - 3320 BC (Saladin)
Test #9 :
Buddism ==> T15 - 3400 BC
Hinduism ==> T16 - 3360 BC (Mansa without FIN used)
Test #10 :
Buddism ==> T14 - 3440 BC (Zara)
Hinduism ==> T16 - 3360 BC (Mehmed letting his city grows on FPs)
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Not so strong Conclusion:
Earliest Buddism date is 3480 BC (T13) reported to human for an AI without Myst.
Earliest Hinduism date is 3360 BC (T16) reported to human for an AI without Myst.
Remainst to test the case a FIN AI working an oasis gunning for Hind.
Maybe 3400 BC (T15) Hindu exist?
Izzy, Zara and MM are terrible zealots just like DanF presented in his list.