Could a classical era or middle ages civilization advance in shipbuilding technology alone and develop ships like carracks that could circumnavigate a world's oceans allowing them to colonize other continents then enter a 'medieval tech' colonial era? Would it require other technologies advancing simultaneously other than developing compasses? Could the Roman Empire, for example, have advanced so far in shipbuilding, and colonized the Americas?
Generally, in many middle ages low-tech and fantasy settings carracks as well as other large ships are not seen though the ships in the GRRM's Game of Thrones world appear to be able to circumnavigate a world if they decided to do so. Most settings depict kingdoms and civilizations primarily passing smaller bodies of water.
The Phoenicians and later Carthaginians were the master shipbuilders of the classical era though the Greeks also developed ships early in this period. The Roman Republic would later develop shipbuilding from the Carthaginians. These ships could not navigate the deep seas. Generally, caravels and then carracks were used in the Age of Discovery and later for colonization.
In the Middle Ages, the Chinese were the most advanced shipbuilders with large junks that would later develop into massive ships compared to European models.
Vikings were likely the first Europeans to discover the 'new world'. Leif Erikson, in particular, led the first known expedition to likely sight North America beyond Greenland. This did not lead to widespread permanent colonization though the Vikings were thought to have established settlements in Vinland known today as Newfoundland.