Can't a country grow its GDP without foreign investment? Whenever various developing countries around the world talk about growing their economies, they talk about facilitating foreign investments and they put so much emphasis on it as if a country's economic growth can survive only if foreigners bring money into the country.

To me this is a cynic and dystopian way of thinking as you are dependent on other country's mercy, and those countries which developed themselves in the 1st phase of industrialization-wave are the only ones who rule the roost.

Is it impossible for a country to grow its economy without foreign investment?
No, you can definitely grow GDP without foreign investment or even trade. 

There are 3 basic ways to grow GDP. One is increasing human capital, which includes increasing population as well as allowing women to work. Basically, anything that increases the number of people in the labor force. 

Second, we have physical capital, which is where foreign investment comes in. This includes machines and computers, etc. 

But both of these eventually have diminishing marginal returns. The final way is innovation, which means more efficient ways to do things, as well as new markets and ways to use goods, etc.

But foreign investment also helps with innovation, especially in developing countries, as the investment usually involves bringing innovation from foreign countries to the developing one.

So while it is not necessary, it is definitely helpful.