The question itself is difficult to answer since the presumption is that there was anything akin to a distinguishable 'Celtic era' or society; and that the earliest attestation of Druids is commensurate with their earliest appearance in Celtic speaking societies. There's not really any evidence to suggest either of these would be true.

A few of the popular misconceptions regarding 'Celtic' are indirectly addressed in this recent post: "Did the Celtic peoples "arrive" in Britain, or did Celtic culture just spread to the bronze-age inhabitants of the island?".

A short answer would be that we don't know exactly when, or even necessarily where, Celtic languages arose. We don't know to what degree certain cultural elements were pervasive among Celtic speaking peoples, and we don't know to what degree the Druids were necessarily a fixture of Celtic speaking societies by definition.

The earliest ethnographic records that discuss Druids do not give any indication theirs is a recent institution, quite the opposite. Every indication, with the caveat that these are often extremely brief or fragmentary accounts, is that theirs was a well-integrated social, political, and religious structure among the societies in which they were documented. For instance from Diodorus Siculus:

As a rule, among all the Gallic peoples three sets of men are honoured about all others: the Bards, the Vates, and the Druids. The bards are singers and poets, the Vates overseers of sacred rites and philosophers of nature, and the Druids, besides being natural philosophers, practice moral philosophy as well. They are considered to be the most just and therefore are entrusted with settling both private and public disputes, so that in earlier times they even arbitrated wars and could keep those intending to draw themselves up for battle from so doing.

And also from Julius Caesar:

The Druids intervene in divine matters; they look after public and private sacrifices; they interpret religious matters: to them a great number of young men rush together for the sake of instruction, for the Druids are great in honour before them. For as a rule they settle all public and private disputes and, if some crime has been committed, or if a slaying done or if it concerns inheritance or a border dispute, the same Druids decide...

The Druids retire from war nor are they accustomed to any taxes. They have immunity from military service and are exempt from all lawsuits. So greatly are young men excited by these regards that many assemble willingly in training and many others are sent by parents and relatives. They are said to commit to memory a great number of verses. And they remain some 20 years in training...

Notably, despite being limited, their attestation is spread amongst several societies across multiple non-mutually-intelligible Celtic languages, and in different periods, making them one of the strongest remaining non-linguistic lynch-pins of the idea of a general 'Celtic' culture; itself an idea that has become otherwise increasingly unpopular in modern scholarship.