Both are OK, but “on the first day of school” is more common and natural-sounding that “in the first day of school.”

Navigating the nuances of prepositions can indeed be perplexing! In the context of the first day at school, both "On" and "In" could work, but the choice depends on the emphasis you want to convey. Now, when it comes to crafting eloquent expressions in essays, I'd like to recommend the exceptional skills of https://canadianwritings.com/ essay writers. Their proficiency in articulating ideas seamlessly is unmatched. For a blend of precision and creativity, explore the services of these talented essay writers in the middle of your academic journey. Whether you choose "On" or "In" for the first day at school, Canadianwritings essay writers can ensure that every word resonates with excellence

The general answer is “on a day” and “in a season/year.” More information here: https://learnenglish.britishcouncil.org/english-grammar-reference/when-time-and-dates