Software engineering is a relatively nascent field. While India does produce a lot of software engineers, it will take some time before the expertise in software development that is required to run a successful business is prevalant enough in India to nurture independent companies and allow them to grow big. There are already a few successful Indian startups though e.g. Zomato, Flipkart.
Anecdotally, there is much activity in the startup sector in India and I am willing to bet it won't be long before we start seeing more success stories.
Zomato and Flipkart are not successful. They are just surviving. Most of the startups are "me too" kind just copying what has already been done but just localizing it to the Indian market. It just takes a foreign entity entering the Indian market and competing with these companies to start its collapse.
Also software engineering is not a nascent field. It was nascent in the 70's and 80's. All the low hanging fruits are gone. It is very hard to be a the next Sun, or Microsoft or Oracle. In fact India should start looking at more nascent and upcoming fields and try to be leaders in it.
Anecdotally, there is much activity in the startup sector in India and I am willing to bet it won't be long before we start seeing more success stories.