Men's Cricket
K L Rahul is the first Indian cricketer to score a century in his debut ODI. He achieved this landmark on 11th June, 2016 against Zimbabwe. Before him, the highest score by an Indian batsman in his debut ODI match was 86, scored by Robin Uthappa against England.
Women's Cricket
The first Indian cricketer to score a century on ODI debut was Mithali Raj. The second Indian cricketer to score a century on ODI debut was Reshma Gandhi. Incidentally, both Mithali and Reshma made their ODI debut in the same match, against Ireland in 1999. Mithali made 114*, Reshma made 104*. And India made 258/0 in 50 overs.