Yes, the Phoenicians existed.

PHOENICIAN WATCH: Did the Phoenicians Even Exist? Everybody in the Mediterranean around 3,000 years ago hated and envied these masters of seafaring, but who exactly were these Phoenicians? (Philippe Bohstrom, Haaretz). As phrased, the first question in the headline is idiotic, but the article is a good and wide-ranging survey of what we know about the Phoenicians. I assume the headline was provided by an unhelpful, clickbait-seeking editor.

The Phoenicians are famed for being master seaman who traded with the peoples around the Mediterranean, spreading their alphabet as they sailed. Yet although they established trade centers as far as Spain and North Africa and founded the city of Byblos, which gave its name to the most influential book ever published, surprisingly little is known about them. Even their name comes from Homer, who dubbed them "Phoenicians", meaning "purple men", a reference to the murex dye for which they were famed.

The Old Testament never actually mentions Phoenicians. The only reference to that name is in ancient Greek writings, and they were referring to merchants living in cities along the coast of modern-day Lebanon.

In other words, the "Phoenicians" mentioned by the ancient Greeks were part of what the biblical authors called "Canaanites", in terms of archaeology, religion and language. There was not much setting them apart from other Semitic cultures.

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Beyond this, it's hard to excerpt the article, so read it all. There are many, many past PaleoJudaica posts on the ancient Phoenicians and Carthaginians. Just run "Phoenician Watch" and "Punic Watch" through the blog's search engine to find them. And also, see here for why the subject matters to PaleoJudaica.