Sails were in common use in the eastern mediterranean from about 2000 BC, but the earliest Egyptian depictions of sails are from a thousand years earlier. We do not really speak of Phoenicians until about 1200 BC, so no, there were sailing boats long before that time. If you want to include older Levantine (Canaanite) populations as 'Phoenicians' then they are amongst the oldest, but together with others, such as the Amorite people of Ugarit, the Minoans, and the Egyptians, for example.

If you are less interested in the 'sail' aspect, the oldest canoes we have are from 6000 BC, but it is quite likely that early settlement of islands (including Australia and Crete) was done by boat deep into the Paleolithic, up to 40.000 years ago.