This is somewhat of an unsolved problem. Some countries actually have tried to boost their birth rates (for no real reason). I want to mention something first:
The declining birth rate rhetoric is often racist at its core. I'm not saying it has to be, a future civilization might actually have that issue. But currently, what a lot of people are talking about is not enough people being born belonging to their kind and dirty foreigners having more babies. One should be aware of that. I'm not saying you are a victim, but you should look into who has been telling you those things and their motives. Most advocates of "more babies" claim the wrong kind of people are multiplying.
Because of that, some countries have tried their best to increase birth rates and nothing has worked directly. I think it is fair to conclude that you cannot have a significant increase in a modern democracy or even in less democratic countries. I will not name examples because people hate it when I do that, but there are some countries which I would not call democratic that have failed. You can certainly increase the birth rate short term (for example by improving the economic situation), but again and again the increase was small and it declined again soon. I will not mention one obvious and large country that will feel this in the near future because let's keep politics outside. Some countries have managed to stabilize their birth rate, yes. But getting it up again, especially to the the levels you implied?
My answer is too long already, if you want to know how to keep it at a certain level, there are already a couple of decent answers. I personally would look into how France treats mothers and children differently than others. Because France exists, this is also a bit off-topic. But they are at a relatively low level globally and not close to your 4 births.
So we are dealing with an unsolved problem here. If someone actually has a solution that would not destroy the country, there are several candidates that would like to implement it.
However, a case can be made that highly developed countries tend to have lower birth rates. This is not the only factor, Germany has a significantly lower birth rate than France (again), two countries on equal development level. Btw, why not make Germany more French? If you know how, you should consider going into German politics, they pay reasonably well. There are many variables here, too many.
So what about destroying your country?
Well, I think this might be your only direct solution for boosting the birth rate if you succeed. If you want more births, go back to the middle ages. But this will not lead to more population. More people will die because of the plague and hunger and dirty water and during child birth - if you succeed. You won't because people will have enough after a year or two. As a result, the birth rate will drop again. Once again, short term.
So consider your only reliable and proven option: Immigration. Remember the people that wanted the dirty foreigners to stay away? Well, if you want more people, do not listen to them. Let them in. If you offer something nice (or just have good marketing), people will want to live in your country. This is happening all over the world right now. And if you do not have enough population increase, just destabilize a poorer country and (mostly young) people will join you by the millions. Let's lookat France (once again): Their birth rate increased (I told you that this cannot happen before) from the 70ies onward? How did that happen? Well, they had a significant worker shortage in the 70ies and then the immigrants came. Ever since there are more children born there. A combination of good politics/protection for mothers/child friendliness/open doors to immigrants/economic growth and one can have an unusual high birth rate and a growing population in a wealthy democratic country.
A word on your 4 children policy: Well, I already commented on this, this one is impossible to implement.