The dating system in the west traditionally counts the years since the supposed birth of Jesus. I understand that historians, or at least those who accept the historicity of Jesus, are somewhat uncertain on his actual birth date, placing it in a few years before 1 CE.
So given this uncertainty, is there a modern way we define years. Do we have a reference year, one event we are sure happened exactly XX years ago, in the ancient era, and so we can reliably count years since then.
To be more clear, imagine I say Jesus died in the year 33 CE. That would be a "credible" date based on the gospel (let's just assume it's credible) but suffers from the flaw that it is relative to another uncertain year. Whereas if I say Caesar died exactly 2064 years ago (ie 44 BC) I may have a more precise way of counting the years before and since. Tangentially, are dates in the ancient world, such as Mar 15 44BC, correct, or are they an estimate of the delta w.r.t. the birth of Jesus (so suffer from error on the zero).
Hope I'm clear! Thank you and happy Saturnalia!
The dating system used nowadays all around the world was devised by a monk that lived in the sixth century, Dionysus Exiguus (the Little). It's the so-called Anno Domini system, who uses as its epoch year (the first year of our Era) the Roman year of the counsulship of Gaius Caesar and L. Aemilius Paullus, corresponding to 1 AD. The Anno Domini wasn't the only dating system in circulation: there was the Anno Passionis, another Christian system devised by Victorinus of Aquitaine (epoch: 28AD, corresponding to the year of Passion/death of Jesus according to Victorinus); the Seleucid Era, a pre-Christian dating system (epoch: 311 AD, the year of the reconquest of Babylon by Seleucus Nicator); Hispanic Era (epoch: 38 BC, the event it specifically refers to is not exactly known, but it's however called the "year of the Pacification of Hispania"); the Byzantine Era, an Anno Mundi system (epoch year: the supposed year of the creation of the world), that was placed, in contrast with the Jewish Anno Mundi, in 5509-5508 BC (the year started in September). These other dating systems continued to be used well after Dionysus the Little's AD system: the Seleucid Era seems to have been used in the Eastern Hellenistic world up to the 6th century of our Era or even later; the Hispanic Era was used until the fifteenth century in the several Christian states of the Iberian peninsula in official or semi-official way; the Byzantine Anno Mundi system was used in Russia until Peter the Great's reign (who in 1700 AD decided to switch to the AD system while retaining the Julian calendar - the Gregorian calendar was introduced in Russia, as it's widely known, only after the Bolshevik revolution). The Anno Domini system began to be used in Western Europe after great scholars like Beda Venerabilis used it in their historiographical and literary works. The precise date and month of historical events is given in the Julian calendar between 8 AD and 1582 AD (after 1582 also in the countries that didn't immediately adopt the Gregorian calendar, like England). Before 8 AD, when the use of leap years in the Julian calendar was stabilized, we use the proleptic Julian calendar: it's like extending backwards the Julian calendar. So, even if Julius Caesar was assassinated after the creation of the Julian calendar (obviously), 15 March 44 BC is still given in the proleptic Julian calendar.
Do we know the date of historical events without depending upon our dating system? Certainly, some events are dated thanks to astronomical phenomena like an eclipse. But the problem is not resolved by that: we can just say X happened exactly 2469 years ago, and exactly 245 years after Y, but we still have the need to put X and Y on a timeline, and thus we are forced to used a dating system. I don't know what you mean with "a modern way to define year". Almost everyone in the world, and historians as well, define years with the Anno Domini system. We know that Jesus probably wasn't born in 1 BC (year zero doesn't exist) like Dionysus thought, we it's impossible to agree on the exact date he was born (btw, virtually ALL historians agree that Jesus of Nazareth really existed, of course secular scholars reject miracles, that are outside the historical method anyways). We could use another historical event, whose date we know from the passage of a comet or whatever, as a new epoch, but for practical and technical reasons it would be really difficult to change the current dating system. Moreover, I can't really think of more important events in history than Jesus' birth, even if I'm agnostic myself, so it wouldn't even be reasonable to change the dating system, but that's a personal opinion.
As a side note, Christmas is not Saturnalia, despite the meme "everything Christian is really pagan", so a Happy Saturnalia, if said unironically, can be wished only to Roman neo-pagans which are certainly not the majority of people nowadays. A happy holidays is certainly more welcome.