Thanks to the people who suggested the Green Line, and to u/rajeshsingh1234 for sharing the station manager contact numbers.
Steps to get the Delhi Metro One Card:-
Call your nearest metro station before heading out to check if they have the Delhi Metro One Card in stock. No need to go there in person just to find out.
If they have it, go directly to that station's customer care and get it.
If not, keep calling other stations (especially on the Green Line) until you find one that has it, then go pick it up.
(Remember, no matter whether you call the station manager or not, some metro stations genuinely don't have the stock and won't be able to provide it to you. So the statement – "it is available in all stations" is wrong)
I had the Airtel Metro Card but I didn't like it much. The DMRC virtual card also has an issue where it stops working if your balance drops below ₹100. On top of that, one day I couldn't enter the station due to a technical error with the virtual card and had to buy a physical ticket instead.