Purple was sort of around. There was a dye derived by clams with a name that sounds like purple by the Phoenicians, Greeks, then Romans, and was more of a red-purple to red, but that eventually evolved into the word we use now. They also attributed it to the color of wine and of all things, the ocean.
Weirdly blue is a pretty rare color concept in the ancient world, and a number of cultures often just combined it with green, or vice versa. The closest to blue as a concept they usually got was indigo, another dye imported from India, and they’d dilute that into woad for a slightly lighter more pastel/ periwinkle blue (it wouldn’t stick as well as true indigo though).
Before the ship it was an old scottish folkstory about a guy going home on a stormy night, encountering a coven of witches, calling out out to one that had a really small shirt (cutty sark) and never being seen again Ichabod Crane style. The figurehead on the ship is what gave the ship it’s name, because it was based on that story.