Does the Gregorian calendar rely on the birth of Prophet Jesus, peace be upon him?

We do not have authentic proof that the Gregorian calendar is linked to the birth date of Jesus, peace be upon him. It is mentioned that the monk Dionysius Exiguus was the one who established a Christian system for dating events, starting from the year he estimated to be the birth of Christ. Muslims have their own calendar, which is tied to lunar months for all their acts of worship and transactions, as Allah Almighty says: "They ask you about the new moons. Say, 'They are measurements of time for the people and for Hajj.'"