India is not a part of NATO. India was one of the leaders of the Non-Alignment Movement, but did certainly bend a little towards the USSR.
USSR and post-USSR Russia has solidly backed India in many issues. When the US imposed bans on export of vaccine raw materials even after a month of assurances of special waivers for India, Russia agreed to supply and produce Sputnik V in a heartbeat.
Historically, here's one example- when US Ally Pakistan was committing a genocide and ethnic cleansing on its own people [0] (now the country of Bangladesh), and India was funding and training the rebels, the US sent Task Force 74 to deter India. And Russia sent cruisers, destroyer, and a nuclear armed submarine to balance the situation.
India won the war of 1971. And the independent country of Bangladesh was born.