I don't really know how fast the Indian government is vaccinating its people but I believe that other countries already started preparing and giving vaccines. Since India has a bigger population, it's understandable for their government to make fast action and start with mass vaccination. But I can't really say if they will have economic advantages since other countries are also working on it. This is not a race where the first country to finish providing vaccines for everyone will have an economic advantage. But obviously, if things work smoothly, not only in India without any problem with the vaccine, we will soon be back to our normal lives.
Yes indeed it is very natural if India takes vaccination measures for its citizens if they are able to distribute vaccines throughout then I don't know what will happen, not only in India, in my area, Indonesia has started vaccinating this to prevent the virus from spreading it continues to spread, even the first president who was vaccinated was to convince the public to want to be vaccinated because some of them did not want to be vaccinated.
Because this also refers to the economy that occurs if indeed the vaccinations are carried out and they are stronger, the economy will be better than before.
But I think it's still speculation and vaccines don't necessarily heal the economy from slumping.