It would have been informative if for example if St Paul in his letters to the various Christian communities had dated them such as “in the 4th year of the reign of…”.
When did the practice of dating letters begin ?
First, Paul’s epistles weren’t “letters” in the traditional sense - that is, a message sent to a specific recipient, to communicate specific information. They were more in the lines of sermons sent to a community, and thus the time they were sent wasn’t a critical part of the message.
Though I have no cites, I suspect that dating was a part of letters and communications from early on. If, say, a field general were writing to the Emperor about troop locations, whether the message was sent on August 1 or August 10 would be a very critical piece of information. Knowing the date something was written was very important when the message could take several weeks (or longer) to arrive.
Hundreds of letters survive from the Roman author Cicero (105-43 BCE). As you can see from the selection here, his letters often included specific dates.
Of course, those are modern translations of the dates. Cicero would have expressed himself using the Roman calendar.