Sure. We can use BCE and CE instead of BC and AD
But still either way, we are still using the dawn of Christianity as the marker to separate eras
The bigger question is - what are some of the alternative years we can use to reset the counter?
As in - we Indians can opt for Vikram Samvat, or maybe something more momentous. E.g. the birth of Buddha, or birth of Adi Sankara, to reset the counter
But it doesn't speak to the rest of the world
Indian alternatives:
Sometime circa 1200 BCE (Kurukshetra war?)
563 BCE (birth of buddha?)
57 BCE (Vikram Samvat)
788 CE (Birth of Adi Sankara?)
1192 CE (Second battle of Tarain)
450 BCE : End of Greco-Persian wars - Crucial Greek victory
622 CE : Birth of Islam
1492 CE : Columbus reaching the New World
1517 CE : Protestant reformation (Luther publishing "Ninety five theses")
1620 CE : Mayflower landing