hi! Sure the Gregorian calendar is from the 16th c, but that was a tweak of the Julian calendar which was introduced 1st c BC (under Julius Caesar), which was itself a tweak on earlier Roman year-reckoning methods, so people were keeping track. I'll leave the details to the experts of Ancient Rome, but you might be interested in the following posts which ask related questions:

• How do we know what years certain pre-gregorian historical events happened in?

• How certain are we of what year it is? Were there every any disagreements, like during the Dark Ages or afterwards, of the exact year?

• If an event is recorded to have occurred on a particular date, and I ask you to say with 100% confidence how many days have elapsed since that event, what is the oldest era for which you can do this?

• What is the earliest recorded date that we can determine accurately?

• What is the earliest reliable documented event in human history?