I think there are two steps: 1) Make people want to have kids. 2) Make it feasible for them to do so.
People already want more kids than they're having, so focussing on (2) at the moment is probably the best approach.
Everyone I know who wanted more kids wanted them before having 1 or 2. And it is almost always the men who wanted more kids, as women are more cognizant of the sacrifices and risks.
And this applies to financially secure couples in the US who willingly stop at 1 or 2.
“Everyone has a plan until they get punched in the face.”
> People already want more kids than they're having
Maybe some people. But nobody I know wants more children. They want a better future for the children they already have. They want to have hope for their future.