There is no sure-fire way of guaranteeing the activation time for new SIMs in India. It depends on back-end systems and document processing and varies depending on the operator. The "2-24 hours" that is mentioned in the other answer is the range of "maximum" times taken by all operators to activate the connection. This range is applicable to all cards (prepaid, post-paid, numbers ported from another operator, numbers ported from prepaid to postpaid or vice-versa, replacement for lost cards etc.) and hence may seem long. The time taken to activate new pre-paid cards is usually considerably less. Vodafone, for example, says activation will happen in a few hours but it usually takes only minutes in my experience.
Indian residents can provide their Unique Identification Number while buying a SIM and this reportedly shortens the activation time considerably as the address and contact details are picked up from that database (There is a debate around the need to link this unique number with your mobile connection and many Indians prefer not to do so but this is not the place to bring that up).
As a foreign tourist, this avenue is not available to you. Your best bet is to buy direct from company stores (Airtel Store, Vodafone store, Jio Store etc), provide complete documentation and request the executive to expedite your case. As already said in the answer to your other question, there are a plethora of such stores in all big cities (and Hyderabad is a very big city) and Google will direct you to the nearest one.
As an aside, since you have a lot of questions about SIM cards in India, you can read this article (mirror) about using India SIM card as tourist for background information.