So the strategy today's developing countries should be following is to find new frontiers in science, technology, entrepreneurship to create wealth while in parallel trying to provide basic facilities to their people. Developing countries are in some ways like startups- Perpetually strapped for cash and resources, struggling to stay afloat and facing tough odds. The key for them is not to try to compete in areas where others already dominate, but to disrupt them (by trying drastically different approaches) or to seek new fields. Microsoft didn't try to compete with IBM in mainframes, they went for the then-burgeoning PC market. Apple is the world largest corporation not because it competes head-on with Microsoft in the PC market, but because it disrupted mobile. Similarly, space is a good avenue for India to compete in, where there are few incumbents and where India can exploit its natural advantages (such as it's eye for cost-saving and huge, inexpensive talent pool).
Updated: Edited to removed lines that detract from main point.