There are plenty of amphibious invasions in early history. The Greeks recorded a very early invasion of Anatolia in the Iliad. The "Sea Peoples", a favorite of AskHistorians, invaded Egypt via boat in 12th century BCE. Caesar invaded Britain in 55 BCE with 80 ships and two legions... and then did it again the next year with five legions, the earlier attempt having been bottled up. The Mongols attempted invasions of Japan in 1274 and 1281 with somewhere between 15,000 and 150,000 soldiers (depending on who you believe.)

Your question in specific recalls the circumstances of the Spanish Armada of 1588, a force transporting some 18,000 soldiers from Spain, and meant to pick up substantially more from the Netherlands. The Spanish Armada, of course, was not successful: weather, disease, and naval opposition make any large seaborne operation difficult, and combined to thwart that particular fleet. While the English fire ships get all the press, the Atlantic (and North Sea) were a major problem. "I sent the Armada against men, not God's winds and waves" said Philip II on learning of the fate of the expedition.

Weather is always a problem for many seaborne invasions. Caesar's first invasion of Britain saw many ships wrecked on the beach due to weather. The Mongol invasion of 1274 was wrecked by a typhoon on the way home, having failed to make a successful beachhead, and the much larger one in 1281 was essentially destroyed, after being repulsed several times by defenders, by another typhoon, the "kamikaze", or "divine wind." Even the modern invasion of Normandy during WWII was planned carefully around weather.

Then there's the issue of logistics. The distance of the Spanish Armada was anomalous, only really made possible by the Habsburg presence in the Netherlands from which the invasion army could be supported much more readily than Spain. Even pre-modern armies require an enormous amount of logistic support, which only a truly prodigious amount of shipping can support at long distance. Most historic invasions happened at shorter distances.

You can't just go sailing about invading places, because it's a rather dangerous way to transport an army and requires a lot of resources to even try, though it can certainly be done, especially at shorter distances. An accurate video game would perhaps limit your distance based on your naval forces (or starve you if you exceeded them), and give you a certain (high) chance of disaster each turn.