He began playing cricket in his childhood at the tender age of eleven, and he began practicing the sport at Gandhibagh Academy in Meerut, where he was coached under the watchful eyes of his maternal uncle Tankeeb Akhtar. In a Ranji Trophy match between Uttar Pradesh and Saurashtra in 2011, Rizvi got the attention of Uttar Pradesh captain Suresh Raina, as the latter was impressed by the fielding efforts of Rizvi, who was only eight years old at the time. Raina eventually spotted the talent in Rizvi and gifted him his sunglasses. It was his maternal uncle, Tankeeb Akhtar, who inspired Sameer to take up cricket seriously, and Tankeeb also faced the wrath of Sameer's father for distracting Sameer from focusing on studies. At one point in time, he stepped up as the main breadwinner of his family at such a young age after his father was diagnosed with a brain haemorrhage in 2020. His father Haseen Rizvi works as a property dealer In December 2023, he was bought for worth 8.40 crore by the Chennai Super Kings in the auction for the 2024 Indian Premier League tournament. The day after being bought for a record price in the 2024 IPL auction by CSK, his house was flooded with media reporters, neighbors and also a local politician in Uttar Pradesh. He eventually became the highest earning most expensive uncapped player in the 2024 IPL auction.