Generations of historians and archeologists have studied this exact question! For such a small country, Ireland has an incredibly rich archeological heritage. One of the foremost scholars on European prehistory is JP Mallory, who spent his career working in Ireland and whose book The Origins of the Irish is the main source for this post.

The Bronze Age lasted somewhere from 3300 to 1300 BC, but in Ireland bronze working began much later than elsewhere. About a thousand years after bronze metallurgy emerged in places like Mesopotamia and Egypt, we see the sudden arrival of bronze-working in Ireland. The arrival of bronze would mark the beginning of an entirely new epoch of Irish history, and the shift from the neolithic to the bronze age would probably be more sudden and rupturous in Ireland than anywhere else in the world.

To step back for a moment, Ireland before the bronze age was a patchwork of complex agricultural chiefdoms. These were the people who built Newgrange and similar megalithic tombs. They were not truly indigenous to Ireland, because their ancestors had initially brought agriculture to the British Isles from the Near East, but the neolithic inhabitants of Ireland had been established for thousands of years. Then out of nowhere, an entirely new set of technologies arrived: bronze daggers and halberds for one, but also new forms of pottery, in particular these mysterious jars or beakers ubiquitous in bronze age tombs.

Why bronze and beakers arrived at the same time in Ireland is a question that's puzzled archaeologists for years. These artifacts are clearly of an ultimate continental origin (just as agriculture was brought to Ireland thousands of years earlier from the continent) yet display some characteristics not seen elsewhere. In the 1960s and '70s, Lithuanian archaeologist Marija Gimbutas revived an older, unpopular theory that the so-called "Bell Beaker people" were connected to the Proto-Indo-Europeans of neolithic and bronze age Europe: a group of nomadic horse-riders from Ukraine and Russia whose early mastery of the horse and the wheel seems to have aided centuries-long migrations across Eurooe and eventually into parts of Asia.

This model makes a lot of sense intuitively: Irish Gaelic is an Indo-European language, so some contact with the continent was necessary for that language or its ancestor to come to Ireland. Because bronze tools and bell beakers existed in France and Spain before arriving in Britain or Ireland, it's plausible that these two movements could have been connected. But doubts persisted, because although the continental spread of Indo-European languages was closely connected to the history of horse domestication, there is no evidence of horses in Ireland during the early bronze age. Irish bronze age artifacts also have a distinctly local flavor, and tend to involve a lot more gold. Mallory was also skeptical that Gaelic had arrived around 2500 BC. Because Primitive Irish had clear similarities to what is known of the Gaulish language at the time of Julius Caesar, it seems unlikely that they had diverged two and a half millenia prior. Mallory took Gimbutas' model, believing that bronze tools were introduced by continental migrants alongside new languages, but did not concur with her opinion that this migration involved large numbers of people, or that the language spoken by these migrants was Gaelic.

Over the past 10 years, genetic evidence has provided what Mallory calls a "magnificent vindication" of Gimbutas' work. It turns out that all the skeletons buried next to bronze tools and ceramic beakers were distinct from the older Irish residents who had built Newgrange. This migration had a far wider impact on Irish genetics than expected, with most paternal neolithic lineages being replaced by migrant lineages. Mallory concedes he was wrong to be skeptical of a major migration to Ireland during the bronze age, but maintains that the language these bronze age migrants spoke was not Irish. Rather, he believes that they spoke a different Indo-European language that was supplanted by an ancestor of Irish during the subsequent Iron Age.

Recent genetic studies in Britain have shown a modest arrival of continental migrants right around the time Mallory expected Celtic languages to have crossed from France into the British Isles. As soon as research is conducted in Ireland, we can get a clearer view of how and when Celtic languages arrived in the emerald isle as well.

Obligatory “you should consider also asking this in /r/AskAnthropology .”

This question would only really be answerable by archaeologists, and I’d strongly suspect the picture of what it would look like to live in Bronze Age Ireland is still frustratingly incomplete. I’d also be willing to bet that there’s not a single written source from Ireland in this period at all to draw historical analysis from. Unless there’s some extremely well traveled Sumerian that I’ve never heard of.