WT, can you confirm your city/worker MM for these first few turns? It sounds like you build a Quechua first working max hammers to get it done ASAP. Once the first Quechua is done, you build another one but switch to max food for growth. The worker then improves food (farm) -> Gold #1 -> Gold #2 and as you grow you work food, gold (assuming it's mined already), gold. Is that right? Or do you continue to work max food until you grow to 3 pops and then work food + 2 golds?
If your goal is to maximize the yield you get from the golds, you want to work farm+mine at size 2. I will measure in hammers and commerce, but if you like you could could measure in gold-turns worked to keep the the numbers simpler albeit with less precision.
There's actually a simple calculation you can do -- work out what you're missing by spending time at the smaller size, and choose the configuration that minimizes the cost.
Let's look at the corn start. Your choices are between:
- 7
1
per turn working rice farm + unfarmed fp
- 4
3
9
per turn working rice farm + gold mine
you need to compare with your target
- 6
17
per turn
(I'm ignoring the hammers/gold from the city tile and commerce from the corn, since you get those either way)
So the two choices boil down to
- You're missing 6
15
per turn over 11 turns = 66
165
missed
- You're missing 3
8
per turn over 18 turns = 54
144
missed
Alternatively, (but ignoring roundoff error due to food overflow), you could divide by the excess food rather than count turns until growth, to measure the "price" of a unit of food:
- You're missing 0.85
2.14
per 1
- You're missing 0.75
2.00
per 1
(yet another alternative for calculation is to cross-multiply; but I find it harder to keep that straight in my head, and isn't as good for comparing more than 2 options)
Either way, you're missing out on more hammers/gold if you do max food at size 2. And both calculations assumed you got the second mine finished in time for growth; working the mine at size 2 gives you extra time to make sure that happens.
Of course, the calculus can change if you're looking to a greater time frame where growth to size 4 matters. You might look at it as having the option to pay 12

21

in order to get to size 4 seven turns early.
The rice start works out that you're missing the same amount either way -- but working the mine at size 2 still means you have more time to get the second mine finished, and it means you get some of your initial Quecha's earlier, which I imagine has value here.
If you actually have so many worker turns available to you that you can have one of the flood plains farmed too, then the rice start is better off working both farms, and the two options give the same result for the corn start.