Outside of an internation airport, getting an India SIM is possible but not easy. Last time it took me an hour, and involved visiting several shops, including one independent shop accompanied by staff from the Airtel store who couldn’t manage it themselves… Very cheap though, INR 500 for 3 months data and local calls, plus INR 500 to the taxi driver so he’d give his details as a reference and agree to receive the activation OTP! At an international airport, it’s normally a bit more expensive (INR 600 to 1000, seemingly at random), but quicker and easier, just a few forms and photos of your passport. Airport sims seem to take longer to activate.
I’ve had very mixed luck getting OTPs to non-indian numbers, the odd airport or big mall might manage it, most places will offer to send them but fail. Some places have workarounds though, eg at Delhi airport you claim your Indian phone number is 1122334455 and your pin is 1234 and it lets you on immediately! (There’s a hand written sign on the information desk in the international arrivals area with these details on)
By far the best option, if available, is to get one of your Indian colleagues / friends to get a sim for you in their name. Some very cheap deals possible
