I never had any trouble finding beef or meat generally in India, though I never looked for a hamburger.
The trick is merely to find the places where the non-Hindu population eats.
Just about everywhere in the country has a muslim minority, except the parts which have a muslim majority (-: One way to spot muslim places is they will often have some signs in Urdu mixed in with whatever the local language might be. And Urdu is easy to spot because it is written in Arabic script. Another way is to see women dressed in muslim hijab.
But muslims are not the only meat eaters in India. Sikhs also eat meat including beef. The Sikh homeland is the Punjab in the north, but there are Sikh minorities all over India and a diaspora around the world. In fact most well-known Indian dishes outside India are Punjabi dishes because the Sikh diaspora were the ones opening the most Indian restaurants around the world. Sorry! I was wrong about Sikhs.
Now Punjabi does use it its own writing but it looks somewhat similar to the Devanagari in which Hindi s written in unless you know what to look for.
An easier way to spot Sikhs is by their turbans.
One more important thing: In tourist areas there will often be restaurants with meat including beef on the menu just for tourists. Avoid the meat in these places unless they are very popular. The problem is that the electricity supply is very unreliable in much of India and because the meat is only used when tourists drop by it may be kept in the freezer. You don't really want to eat meat that's thawed and re-frozen a dozen times.
So when you want to eat meat in India, look for restaurants where there are women wearing hijab, men wearing turbans, or signs in Arabic or Punjabi script if you know what they look like.