What are the conditions that force any government to formulate population policy?
No condition can literally force a government to adopt a population policy. Governments that do adopt such policies do so because they think it is best, not because they are literally forced to. Governments tend to adopt such policies when they think that their population is either growing too rapidly or is in serious decline.
One force that can encourage a government to institute a population policy is an excessively rapid increase in population. This often happens as modern medicine and better living conditions reach a country, making it more likely that women will have many children and those children will survive. This tends to create a surge in population until/unless the country’s culture changes to prefer smaller families. When this happens, countries might feel that a population policy will be necessary to reduce population growth.
A second force that can encourage a government to create a population policy is economic and social modernization. Worldwide, it has become clear that birthrates in countries drop when the countries become richer. This is particularly true in post-industrial countries. This has led, in many countries, to a situation where birthrates drop below replacement rate. That means that the country’s population will decline over time if nothing is done. This frightens many governments as it tends to mean that there will be fewer people of working age to care for/fund the older, larger, generations after they retire. This can bring about policies that are meant to encourage procreation.
Thus, governments tend to institute population policies when their populations rise too fast (usually because health has improved without cultural changes) or when their populations’ growth rates drop too far (usually because the countries become richer and more modernized).