I don't think Bitcoin got anything to do to help people escape poverty, not as long as they bought Bitcoin and threat it as an asset or investment, but overall I really don't see any aspects that it can help people to escape poverty. But in terms of financial services, yes Bitcoin is really capable of that, which is the most goal of Bitcoin having the freedom and we will have our own bank in our pockets.
Assuming, developing countries have what it takes to mine bitcoin, with that, more income people of the countries will earn. The miners will convert some of the bitcoin to fiats and use it to buy something in their community, thereby helping others in the community. If people of developing countries have invested in bitcoin as far back as 2015, it would have brought them earnings too, it will surely affect their counties positively, how about the custodial services like exchanges, if some developing countries have it, it will help them to provide employment. Bitcoin brings wealth to nations, if people of the developing nations embrace it, it will bring them wealth.