There is archaeological evidence that tells us the Druidic presence was well established in the 3rd Century BC and much that suggests that they went back as far as the 2nd Millennium BC. The earliest written source for the Druids are the writings of Timaeus, but unfortunately they only survived in quotations from later writers like Pliny & Siculus. Timaeus' contemporary, Pytheas of Massalia contributed to Timaeus' source writing with primary accounts of Druids. Although no writings of Pytheas are known to exist on Druids, he would definitely have encountered them He was widely travelled in the Mediterranean, and was the first to write of Britain, and describes his circumnavigation of the Islands, so he was contemporaneously accurate. Much of the next accounts are from Posidonius, whose Histories, (now lost) was widely quoted, and seems to be the main source from which Strabo and Siculus wrote their accounts of Druids and Celts.
However, the non-written archeological and cultural evidence for Druids goes back as far as the Chaldeans, and the Assyrians.
Pytheas tells of the British Druids being a Moon Worshipping Cult, and this is borne out by the Coligny Calendar, attributed to the Druids which is unusually, a Lunar Calender. This was the method that the Magi and the Chaldeans used rather than the less complex Solar Calendar that the Greeks and European Celtic peoples were using at that time.
This Calendar can trace it's Lunar roots back to the Assyrians in the 3rd millenium BC, which suggests the Druids had cultural ties in Mesopotamia.
They also were recorded as having the belief in Transmigration of the Soul and of the Souls immortality, an entirely alien and contrary idea to the accepted Greek view, but it was a view that suddenly found popularity with the Pythagoreans in the 6th C.
This is indicative of a link between the Ancient Druids described by Pythea in the 3rdC Bc to the Pythagoreans, nearly 900 years later.
And the Orphic Mysteries pick up this transmigration of the soul as well, which ties in with what little is known about the Druid's religious beliefs.
The Mysteries of Isis, the slaying of Osiris, and the Birth of the Child Horus or the New Sun, takes place using the same Lunar based Calendar as the Druid's Coligny Calendar. And this Calendar seems to have been followed throughout the Mediterranean in the Mystery Schools of the Ephesians, the Attic mysteries of the Phrygians, the Mithraic religion of the Roman Legions, the Cabiric rites of the Samothracians. The unifying factor in these traditions is the Death, and rebirth of the Solar Principle, and is dependent upon the Lunar Calendar's accuracy for predicting the correct points of the year.
Solstices, Equinoxes, and quarter day festivals were all an Agricultural people like the Celts needed to get by on. Yet the Druids had extensive knowledge of Astronomy, which didn't figure into the Celtic Calendar. But did in the Ptolemaic and the Chaldean's more Maritime Cultures. And I think this is the clue that says the Druids had knowledge sourced from a cultural base that was not shared by the Gaul;s/Celts. There isn't any evidence to say that the Druids were even Celtic peoples. The Romans found that the Druids were present, as a separate Caste of intellectuals, throughout the lands of the Celts, and Gauls. The nomenclature Celt, was pretty much interchangeable with that of Gaul as far as the Romans were concerned. They made no cultural distinction between them. But the Druids were present all through the Tribes, as a Philosophical and Intellectual Caste, serving what we might say was an Administrative role. Not part of the Ruling Class, but not without influence either.
Celtic and Egyptian culture had links through the Seafaring Chaldeans, who had trade routes from the Black Sea, across the Med, right up into Scandinavia. And along these routes sprang up many places of learning. They definitely traded in Britain, from the early 1st Ml BC, and there are contemporaneous Temples dedicated to both Egyptian, and Greek Mystery Schools among the earliest places in what is today's London. The Tower of London is built over an ancient Temple dedicated to Apollo. There was also a Temple of Thoth/Hermes, and there were other Temples all along the Thames. Or the Isis, as it was called back then. A short stretch of the Thames is still called the Thamisis today.
And nowhere is it directly recorded that Druids were any kind of Priesthood.