You get 22 rainbow stones per batch pull. The absolute cheapest rarity growths are 4-slot/5-skill gacha golds which require 500 rainbow stones. That's 23 batch pulls or up to 1150 FG. More common girls can cost up to 750 rainbow stones. Getting enough for a single girl simply will not happen in a reasonable timeframe without paying.
How close is Nutaku to finishing the blooming backlog?