There's no year 0, it starts at year 1 CE (Common Era, you may also see this written as "AD 1", Anno Domini 1). The concept of zero is relatively recent, it didn't exist in its current form when this year numbering system was established.
If you go back one year from there you hit 1 BCE (Before Common Era, also written 1 BC, Before Christ) and start counting up one for each year you go back.
So, 2022 years ago is 1 CE; 2023 years ago is 1 BCE; and 2024 years ago is 2 BCE.
That's an interesting question and not something I think I can fully answer, but it seems likely.
AD did come first when the year numbering system was first created in 525 CE since the system was based on an estimate of the birth or conception (unclear which, there's some debate) of Jesus Christ; hence the name "anno domini" ("in the year of the lord"). I'm not sure when BC was first used since that's English rather than the original Latin.
CE (originally meaning "Christian Era") wasn't popularised until ten or so centuries later. It's more popular now in part due to the fact Common Era is less overtly Christian-centric.
Interestingly, ISO 8601 (objectively the best and most correct way to write dates, fight me) doesn't use AD or CE, the standard just counts normally. So you'd go from year +0001 (1 CE) to +0000 (1 BC) to -0001 (2 BC). I guess that means I'll have to change my original answer; there is indeed a year 0 in the Gregorian calendar depending on the way you represent years.