How was sheet metal used to create armor created in ancient to medieval times?

The simple answer to the question 'where did medieval armourers get sheet metal to make armour' would be 'they didn't' - because sheet metal, as we know it, didn't exist in the past. But this is in its own way misleading - the real answer is much more nuanced.

First off though, let's analyze my glib answer above and look at the ways in which it is true. Sheet metal, as we know it, is -rolled- material. Basically, iron or steel in some form is drawn through a series of rollers to flatten it into sheets. The thickness of the metal is uniform because the rollers are set to produce that thickness, so modern sheet metal has a series of very narrowly defined thicknesses (measured in 'gauge' - the area of a plate required to make a pound, lower is thicker -, or in metric measurements, generally millimeters and fractions therof). It is also metallurgically homogenous - the distribution of iron and alloying materials is constant throughout. Put simply, modern sheet metal is a very uniform, regular product whose chemical composition and thickness is exactly specified.

Needless to say, armourers of the late middle ages and earliest modern period didn't have access to this kind of sheet metal. Indeed, in general they didn't have access to rolled sheets of metal in general - rolling sheets of steel/iron to make armour out of wasn't widely done until the 17th century or so, though we know that rollers were used for other purposes earlier, so they may have been occasionally used. Instead, the main, generally the only way to make a flat plate out of a medieval or early modern billet/ingot/hunk of iron or steel was to flatten it with hammers. And flattening steel with hammers produces a plate that is much less uniform in thickness than flattening it with rollers does. Moreover, since the initial metal would be less homogeneous (because of the vagaries of medieval and early modern steelmaking), the resulting plate would be less homogeneous as well. But who would hammer out the plate, and how would they do it? This is where the answer gets more complicated, and interesting.

When I say 'flatten the plate with hammers' you and probably everyone reading this would immediately assume that I mean hand-held hammers wielded by muscular, sweaty dudes. And this was indeed often the case. But by the end of the Middle Ages, that wasn't the only option. In addition to hand-hammering, medieval metalworkers could also use water-powered trip hammers to work out the impurities in blooms of iron, shape the blooms into ingots and shape those ingots into flat plates - indeed they may have also sometimes used them to do the rough work of making the plates into armour! In other words, late medieval and early modern metalworking was at least sometimes pretty mechanized - they would use water power to power the bellows of their bloomeries and blast furnaces to make iron and steel, they would use trip-hammers to shape the steel, and they would use water-powered polishing wheels to polish it smooth. Compared to our image of some humble village blacksmith slaving over armour, this is a far more industrial sort of work than we might imagine - and armouring was, make no mistake, quite an industry, dominated by large workshops operating in big cities, as well as by smaller producers in medium-sized cities working for smaller markets. But let's back up again. What the hell is a trip hammer? Basically it's a big heavy hammer that has a shaft that is raised by a kind of ratchet attached to a water wheel. When the wheel turns enough the hammer is tripped and slips out of the cog that's lifting it and falls down with the force of all of its several hundred pounds. Like this.

Now who would flatten the plates? This depended. Sometimes armourers might prefer to work from billets or hunks of iron/steel called 'osmunds' and flatten the iron/steel out themselves to exactly control the thickness. We know they did this because they ordered billets and 'osmunds' and their neighbors complained about them flattening osmunds at odd hours (no, seriously, this is a real court case from London in the 14th century - I shit you not one of our sources is a medieval noise complaint). But we also see some armourers, particularly later, buying plates of steel that someone else had flattened, probably using trip-hammers. These would still probably be pretty damn thick, significantly thicker than the armour that they would be made into, but this allowed armourers to determine the thickness more precisely and make sure that the parts that needed to be thick were thick and those that didn't were thinner to save on weight. Unlike modern armour made from homogenous sheet steel, late medieval and early modern armour is of a variable thickness, and this is a feature, not a bug - it makes it strong where it needs to be, and light where it doesn't need to be strong.

Anyway, that's a long answer to a simple question, and that's just scratching the surface of a fascinating and multi-faceted late medieval industry.

Sources:

Nicholas Dupras - Armourers and Their Workshops - The Tools and Techniques of Late Medieval Armour production

Alan Williams - The Knight and the Blast Furnace

Matthias Pfaffenbichler - Armourers