When a company is still loss-making, what are some scenarios where you would still invest in them?

Well it depends on why they are making losses. Is it because they are using these profits/earnings to re-invest into other areas such as sales& marketing? If so, I would go 1 step further to chec kon other metrics of the businesses such as skin in the game, management behaviour, TAM.

For some of these loss making business, it's at the early stages, once they have build up their customer base, this cost will disappear, which will lead to exponential earnings growth!

It does depend on the nature of the company and why they aren't making money. Many of times loss-making companies are actually growth companies that eventually spur in stock prices. Take a look at Tesla, negative EPS but bam! 100% growth in share price in a month simply because their expansion in China coupled with announcements of new models of their trucks.

I would invest in the company making losses if: i) The industry it is in is turning around, this signifies the possibility of its current losses turning into profits, ii) a potential sale of its assets and that it is trading below book value. One good example in recent times is Broadway Industrial, the company is constantly making losses but has a book value of 15+ cents, it is looking at corporate actions to spin off or merge its assets with other companies. This signifies a potential relisation of its full 15+ cents and this is why Broadway Industrial share price has gone up 250% over the past few months

Balance sheet, potential / future orders, industry trend