Does a crown have to be a gold or silver crown with jewels, or can it be made of other materials, so long as it represents authority?
In the latter case, it would be very hard to tell the difference between fancy hats and hatlike crowns.
Ancient Egyptian crowns came in many designs and weren't always made out of metal. In fact the materials they are made of are unkown in many cases, since there are no surviving examples and it is hard to guess the materials.
Here is a link to an image of Cyrus the Great wearning an Egyptian hemhem type crown, as well as wings.
Achaemenid kigns and nobles had crowns of various designs.
Another ancient royal symbol was the diadem, sometimes a cloth ribbon warped around the head, and sometimes a metal object with the same shape.
The word derives from the Greek διάδημα diádēma, "band" or "fillet",1 from διαδέω diadéō, "I bind round", or "I fasten".2 The term originally referred to the embroidered white silk ribbon, ending in a knot and two fringed strips often draped over the shoulders, that surrounded the head of the king to denote his authority. Such ribbons were also used to crown victorious athletes in important sports games in antiquity. It was later applied to a metal crown, generally in a circular or "fillet" shape. For example, the crown worn by Queen Juliana of the Netherlands was a diadem, as was that of a baron later (in some countries surmounted by three globes). The ancient Celts were believed to have used a thin, semioval gold plate called a mind (Old Irish) as a diadem.3 Some of the earliest examples of these types of crowns can be found in ancient Egypt, from the simple fabric type to the more elaborate metallic type, and in the Aegean world.4
A diadem is also a jewelled ornament in the shape of a half crown, worn by women and placed over the forehead (in this sense, also called tiara). In some societies, it may be a wreath worn around the head. The ancient Persians wore a high and erect royal tiara encircled with a diadem. Hera, queen of the Greek gods, wore a golden crown called the diadem.
By extension, "diadem" can be used generally for an emblem of regal power or dignity. The head regalia worn by Roman Emperors, from the time of Diocletian onwards, is described as a diadem in the original sources. It was this object that the Foederatus general Odoacer returned to Emperor Zeno (the Emperor of the Eastern Roman Empire) after his expulsion of the usurper Romulus Augustus from Rome in 476 AD.
In ancient times, people also wore wreaths.
A wreath (/riːθ/) is an assortment of flowers, leaves, fruits, twigs, or various materials that is constructed to form a ring.
Ancient people wore wreaths of various plant materials, and also wore gold or silver wreaths imitating the forms of those materials.
I have seen an exhibiiton of the treasures form the Maceonian royal tombs at Vergina, including at least two golden wreaths.
There are also the rare golden hats from Brozen Age Europe:
Golden hats (or gold hats) (German: Goldhüte, singular: Goldhut) are a very specific and rare type of archaeological artifact from Bronze Age Europe. So far, four such objects ("cone-shaped gold hats of the Schifferstadt type") are known. The objects are made of thin sheet gold and were attached externally to long conical and brimmed headdresses which were probably made of some organic material and served to stabilise the external gold leaf. The following golden hats are known as of 2012:
In the 5th to 7th centuries AD, gold and silver crowns were used in the Kingdom of Silla in Korea:
I have seen a display of some of those crowns.
Of course the most pertinent information would be information about ancient Mesopotamian crowns.
The royal tombs unearthed at Ur contain many treasures.
Especially the discovery of the Royal Tombs has confirmed its splendour. These tombs, which date to the Early Dynastic IIIa period (approximately in the 25th or 24th century BC), contained an immense treasure of luxury items made of precious metals and semi-precious stones imported from long distances (Ancient Iran, Afghanistan, India, Asia Minor, the Levant and the Persian Gulf).6 This wealth, unparalleled up to then, is a testimony of Ur's economic importance during the Early Bronze Age.
The tomb of Queen Puabi had at least two gold and jeweled headdresses.
Queen Puabi wore an elaborate headdress of gold leaves, gold ribbons, strands of lapis lazuli and carnelian beads, ...
...An ornate diadem of thousands of small lapis lazuli beads with gold pendants of animals and plants was on a table near her head...
Apparently jewelry of Neo-Assyrian queens from millennia later has also be found:
And no doubt there are many depictions of the headdresses and possible crowns of Babylonian, Assyrian, and other Mesopotamian rulers.