Magician here. Sleight of hand is probably one of the oldest performing arts. Penn & Teller did a three-part series on ancient magic, in which they travelled to Egypt, India and China to see traditional magic. In the Egyptian leg they travel to the tomb of Beni Hasan(2500 BC), where a painting on the tomb walls depict what appears to be an ancestor of the cups-and-balls routine.

Many of the miracles in Egyptian and Biblical religions(e.g. sticks-to-snakes) are disappointingly straightforward conjuring tricks.

Although Egyptian magic is a bit murky, conjuring definitely had a presence in Ancient Rome and we have plenty of evidence of cup-and-ball, juggling and other vanishing/production routines. Christianity was a bit of a problem--people performing magic in markets/squares couldn't exactly refute witchcraft accusations, without also spoiling the game. Magic was in the dark ages(so to speak) until 1584, when Reginald Scot, the masked magician of his day, spilled the beans in The Discoverie of Witchcraft, which you can read here

Many of the routines Scot described use plots that are still common today, especially card tricks: "How to deliver out foure aces, and to convert them into foure knaves" is still, with variations, a regular appearance in closeup magic, as is the classic effect of making a selected card vanish "into a kernell of a nut or cheristone. " There are also descriptions of props, of the same sort you can get in a magic store today: "Boxes to alter one graine into another, or to consume the graine or come to nothing." There are very primitive instructions on audience control and even elements of slapstick, like "how to rap a wag on the knuckles."

Here's how people used to do an old classic, the cut-and-restored rope:

BY a devise not much unlike to this, you may seeme to cut asunder any lace that hangeth about ones necke, or any point, girdle, or garter, &c : and with witchcraft or conjuration to make it whole and closed together againe. For the accomplish- ment whereof, provide (if you can) a peece of the lace, &c : which you meane to cut, or at the least a patterne like the same, one inch and a halfe long, & (keeping it double privilie in your left hand, betwixt some of your fingers neere to the tips thereof) take the other lace which you meane to cut, still hanging about ones necke,/ and drawe downe your said left hand to the bought thereof: and putting your owne peece a little before the other (the end or rather middle whereof you must hide betwixt your forefinger and thombe)making the eie or bought, which shall be scene, of your owne patterne, let some stander by cut the same a/sunder, and it will be surelie thought that the other lace is cut ; which with words and froting, &c : you shall seeme to renew & make whole againe. This, if it be well handled, will seeme miraculous.