India played their first ever international match in a test match on the 25th of June, 1932 at Lord's cricket ground. In that match, C.K. Nayudu created history by being declared the first ever captain of the Indian cricket team post-independence. That day was a historic and a proud day for our country.
Hope this answers your question.
Image Courtesy: Google
Also Read- which year when ipl play for the first time?