The answer to this question depends upon what you mean by 'plate armour.' Many armours from a number of different cultures feature large metal plates forming a rigid or semi-rigid protection. This includes bronze age and classical cuirasses, the Roman Lorica Segmentata and various forms of armour in East Asia and India. Some of these date back thousands of years, and date outside of my specialty.

You can also define plate armour more narrowly, as rigid armour made of interlocking, articulated plates or iron or steel that covers the wearer while allowing for movement. Essentially, a flexible exoskeleton of steel plates that are connected to each other. This form of armour is more particular to western Europe, and developes from earlier forms of supplemental plate protection by the early 15th century (a development process that takes more than 150 years. I write about this history here.

The technological background of plate armour is complex. I talk about it here. Keep in mind that plate armour's development is not a simple story of a single technological breakthrough, and isn't simply the story of developing better tech - it also requires 'end users' who have a use for full plate armour, and these in turn are the result of contemporary tactics.