Sounds good.
Note that if we do have access to water, irrigated grassland with game will produce four food & zero shields. Mined grassland will produce 3 food and one shield - Hopefully one of those is a bonus grassland! For the plains, a game on mined plains will produce 2 food and two shields, and on irrigated plains its 3 food and one shield. (Despotism penalties considered as well)
So: Assuming access to fresh water for irrigation:
Turn 1:
Size 4: Work city center, grassland with irrigated game, grassland with mined game, 2x mined bonus grassland: Food = 13 (net = +5), shields 6.
Turn 2:
Grow to 5 (2 shields bonus on growth) Work city center, grassland with irrigated game, grassland with mined game, mined plains with game, 2x mined bonus grassland: Food = 15 (net = +5), shields 8 (cumulative = 6 + 2 bonus + 8 = 16)
Turn 3:
Size 5 Work city center, grassland with irrigated game, grassland with mined game, mined plains with game, 2x mined bonus grassland: Food = 15 (net = +5), shields 8 (cumulative = 24)
Turn 4:
Grow to 6. Settler produced.
Note that this was a quick check to prove that we can do a four-turn settler factory at size 4 => 6. can look at more options once we find-out if those grasslands are bonus ones.
However, the unit factory idea is a possibility!