Wealthy MENA countries functionally does this, and their TFR is either below replacement or trending to below replacement. And they have other pushers like religion and cheap migrant labour / nannies to incentivize large families.

The TLDR is I think state demographic planning cannot positively incentiivize >2 kids. Unless cohort is extremely trad/religion pilled to have as many kids as possible.

At some point need to negative incentivize, i.e. taxes, limits on wealth transfer or additional burdens for not hitting family quota. Probably even more unsavory demographic programs, i.e. birth increased by 2% after roe vs wade overturned. But forcing people to start families is harder than forcing them abort.