Sadly no he's only dreaming of reincarnating but in reality before he goes to military he went and took his entrance exam again and you can see he's 2 years older than all the freshman basically he's a senior in but if he's reincarnated it would probably starts in middle/high school (and he probably won't be 2 years older than the freshman but, the same age as them) ╮( ̄▽ ̄)╭
OH and on page 7 (this is probably the mostt confusing thing) at first he said "and after returning to the university freshman are two years younger" and after that he said "when I was 20 they were 13" so.. Is he 22 or 27 he keeps changing he's age? Or is it really a time leap? But he said this is NOT a time leap genre manhwaa arghh.. I'm stressed now
It's not a time leap, it will be clearer on ch.2 right away.
The girl also said at the end he wanted to get close to ML since they're on the same age, meaning they both are not true freshman.
Link to the next chapter :
https://catonhead.com/manga/pure-love-hippocrates/volume-1/ch-2/

Girls reincarnate but now boys reincarnate too! Gender equality ╮( ̄▽ ̄)╭