As GP states, heavily pushing subsidies has not been shown to work.
The one thing we know works is restricting access to birth control - I'd bet good money that ups the birth rate in no time. Leave as an exercise for the reader whether it is a good idea xD
Subsidies only come into affect after you have children. They can not work alone society has a much greater affect. They work wonders at making parenting possible while being part of the work force. You only get the subsidies when you have children, the question is how you are supposed to feel secure enough to have children.
These days, the big factors include not having dealt with climate change: parents are being asked to make a big gamble that the future will be better, and having all of the evidence suggest otherwise is a widely-cited deterrent.
It's a problem, because it's raised the bar for expected supervision effort, likely far beyond what is really needed.
if you are chasing a career, putting in 40,50,60 hours a week - how can you take time off to have a kid? who is going to take care of the kid?
Increasingly having kids has gotten more expensive - housing, childcare costs, and general expected investment/supervision of children. In agricultural societies, kids often helped out with the farming; send them to school and they are around less to help. Say that kids can't roam around outdoors unsupervised, and caregivers have to spend even more time watching (older) children. Etc. And as people increasingly move further from where they grew up to chase good jobs, that means they are on average further from their families who would have helped with childcare in previous generations.
The economic realities factor in too - people are waiting longer to get married because they want to date financially stable people, and financial stability is on average taking longer to achieve. But if you had to move to a more expensive city, further from family... that's a recipe for couples where both work and perhaps have to work to make their finances work. Babies have become a luxury item in these higher cost of living places.
if we want more children, we need to make it easier to be a parent. Cheaper / free childcare, better parental leave policies, and cheaper cost of living so that people who want to be stay at home parents can have that option.