To understand the history of caramel, which you're right is hard to find (and I'm not sure if I found enough to fully answer your question), you have to first understand how it is made. That process is called Caramelization

This is where wikipedia is helpful with it's compendium of general knowledge

"The process of caramelization consists of heating sugar slowly to around 170 °C (340 °F). As the sugar heats, the molecules break down and re-form into compounds with a characteristic colour and flavour."

So to try to find the history of caramel you have to understand the history of sugar. And you're right that history of sugar in Europe is tied to the history of sugar in the Arab/Islamic world.

“In the fields of the plains of Tripoli can be found in abundance a honey reed which they call Zuchra; the people are accustomed to suck enthusiastically on these reeds, delighting themselves with their beneficial juices, and seem unable to sate themselves with this pleasure in spite of their sweetness. The plant is grown, presumably and with great effort, by the inhabitants. . . . It was on this sweet-tasting sugar cane that people sustained themselves during the sieges of Elbarieh, Marrah, and Arkah, when tormented by fearsome hunger.22”
Sidney W. Mintz. Sweetness and Power. p. 80

Sidney Mintz uses this Crusader's recollection about sugar in Tripoli to make a larger argument in his classic work, Sugar and Power that

“The Arab expansion westward marked a turning point in the European experience of sugar. Between the defeat of Heraclius in 636 and the invasion of Spain in 711, in less than a single century, the Arabs established the caliphate at Baghdad, conquered North Africa, and began their occupation of major parts of Europe itself. Sugar making, which in Egypt may have preceded the Arab conquest, spread in the Mediterranean basin after that conquest. In Sicily, Cyprus, Malta, briefly in Rhodes, much of the Maghrib (especially in Morocco), and Spain itself (especially on its south coast), the Arabs introduced the sugar cane, its cultivation, the art of sugar making, and a taste for this different sweetness.” p. 73

Others including Sato in Sugar in the Social Life of Medieval Islam, confirm that it was the Arab conquests that brought sugar production from Iran and Iraq, which had come from India, to the Mediterranean and Europe.

One more bit from Mintz is helpful when we try to go from sugar to caramel

“The sugars of the Arabs were no single homogeneous substance; from the Persians and Indians, the Arabs had learned a variety of sugar types or categories. We know about these various sugars and even something about the processes of their manufacture, but the details remain vague. ” Sidney W. Mintz. Sweetness and Power. p. 78

When we look at what type of sweeteners the medieval Muslim was using in the fantastic translation of a tenth century cookbook of Ibn Sayyar we find

"Sugar, bees’ honey, red sugar, and honey ('asal) made from sugar..."

This red sugar and honey from sugar each seems like possibilities

Nawal Nasrallah the editor and translator of the cookbook provides the following notes on this honey from sugar

"asal qasab (عسل قصب) sugarcane honey, which is molasses produced in the process of making cane sugar, as follows:
Sugarcane juice is strained, boiled down into thick syrup then drained and filtered in cone-shaped clay vessels. Cane syrup will drip down through three holes in the bottom of the vessels, leaving unrefined crystallized cane sugar in the cones. This dripping syrup is asal al-qasab, also called quã§ra (ُقطارة), which is molasses (al-Hassan and Hill 222).

asal al-sukkar (عسل السكر) syrup made from cane sugar"

this seems most likely molasses

and this is what she says about red sugar

"sukkar ahmar (سكر أحمر) literally ‘red sugar,’ it is unrefined crystallized brown cane sugar, sometimes used instead of white sugar because it is stronger in properties (hotter and moister). The darker it is, the stronger these properties are."

So, maybe? But if we look at other entries in her glossary we find something that looks close

"fanidh (فانيذ) fanid (فانيد) pulled taffy, chewy sugar-candy, usually shaped into small discs. Medieval sources briefly describe it as cane juice boiled down to thick syrup and then made into fanid. Besides enjoying it as candy, it is used as a substitute for sugar as in some wine recipes. For medicinal purposes, it is mixed with different herbs and spices and chewed to cure coughs and cold-related ailments (Ibn Sina 342)."

This is also a maybe, but probably our best bet.

So this is where history is hard/fun/collaborative. I would love to hear from Western historians, but I would say that sometime between 700 and 1000, the Arabs were heating sugar and probably made something like caramel. And sometime after 1000 in the interactions between Europe and the Arabs/Muslims that transferred and sort of floated around until the industrialization of Europe and then the industrialization of caramel making.

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Sidney Mintz, Sweetness and power : the place of sugar in modern history, Viking 1985

Nawal Nasrallah ed. trans. Annals of the Caliphs’ Kitchens:Ibn Sayyar al-Warraq’s Tenth-Century Baghdadi Cookbook, Brill 2007

David Waines, FOOD CULTURE AND HEALTH IN PRE-MODERN ISLAMIC SOCIETIES, Brill 2011

Tsugitaka Sato, Sugar in the Social Life of Medieval Islam, Brill 2015