Full plate armour is a lot older than the Late Medieval period. The Dendra panoply, a Mycenaean design dated to the 15th century BC, is the earliest example; it may be representative of the sort of full body armour worn by elite warriors conveyed to the battlefield on chariots. Modern replicas show how it would cover most of the body in overlapping bronze plates.

In the Roman period, several kinds of full plate armour are known. In the East, the comprehensive plate-and-scale armour of Iranian cataphracts inspired the outfit of the late Roman heavy cavalry known as clibanarii - their name meaning "little ovens". In terms of their equipment, these men are regarded as the spiritual predecessors of Late Medieval mounted knights. In the West, meanwhile, additions to the legionary's segmented plate armour occasionally led to the fielding of men covered head to toe in steel, as in the case of the rebellion of the Aedui in AD 21:

There were forty thousand, one fifth armed like our legionaries; the rest had spears and knives and other weapons used in the chase. In addition were some slaves who were being trained as gladiators, clad after the national fashion in a complete covering of steel. They were called crupellarii, and though they were ill-adapted for inflicting wounds, they were impenetrable to them.

-- Tacitus, Annals 3.43

This heavily armoured infantry was used as an immovable front line in battle against the Romans. However, they proved a disappointment against their determined opponents:

The men in armour were somewhat of an obstacle, as the iron plates did not yield to javelins or swords; but our men, snatching up hatchets and pickaxes, hacked at their bodies and their armour as if they were battering a wall. Some beat down the unwieldy mass with pikes and forked poles, and they were left lying on the ground, without an effort to rise, like dead men.

-- Tacitus, Annals 3.46

The fate of the crupellarii explains why full plate armour was not universally adopted as soon as it became technologically feasible. In the specific conditions of pitched battle in this period, heavy armour made warriors too inflexible, and put them at a disadvantage against more lightly armed and mobile troops. As a result, despite their immunity to ordinary weapons, they achieved nothing.

There were many factors besides technology that determined whether there was any advantage in adopting full plate. You'll notice that its use in all periods was due to very specific tactical conditions. In Mycenae, the fact that elite warriors probably didn't have to do much walking allowed them to deck themselves out in very heavy and unwieldy armour. In Gaul, extremely heavy infantry was thought to provide an answer to the lethality of a disciplined Roman legion in close combat. In the Eastern Roman Empire, the enemies of Rome largely fought as horse archers and heavily armoured lancers, forcing the Romans to respond in kind. In Medieval Europe, changes in close combat methods along with the rise of effective missile weapons such as crossbows, longbows and firearms led to an ever increasing need for all-round protection. Unless such conditions were present, the cost, weight, discomfort and awkwardness of full plate armour was unlikely to make it a favoured choice. And efforts to improve the available designs of plate armour were obviously only made in periods when it was widely used; why try to fix a concept that no one has any interest in applying?

In short, the adoption of full plate armour was not a question of technology or "scientific advances", but of prevalent tactical conditions and the related priorities of warriors in terms of self-defence, manoeuvreability, comfort, reflection of status, and so on.