The Arabs (or whoever was in their areas) used and still use a lunar calendar. I'm not sure who tought who but theirs sound a bit more precise than what you described (Don't ask me how it works, I don't know details).

Also, is it a coincidence that Ramadan (a lunar month where muslims fast during it each year) started with the new year? I'm sure there's some mythological connection between the two?

Gregorian Calendar used the birth of Jesus

As far as I know, the birth of jesus used the Gregorian calendar, if that makes sense?

Edit: oops posted by mistake.. Damn phone, I sit on it while trying to get up and it published.. oh well, guess those were enough questions for to day 😛

Edit 2: Happy Hindu New Year to you too 🙏

Edit 3: Nevermind, just edited for fun this time! ✌