肯定是用 on，因为是指具体的某一天。比如：

on the first day of school 开学的第一天

The rent is payable on the first day of the month. 房租应在每月的第一天支付。

McArthur opened the bowling on the first day of the match.  麦克阿瑟在比赛的第一天开了球。

Don’t spend all your money on the first day of your holiday!  别在度假的第一天就把钱都花完了！

It was Chinese women who stole the show on the first day of competition. 比赛的第一天中国女队表现抢眼。