I'll start off by mentioning Aioli, which is garlic and oil blended together and is almost 2000 years old having been a popular sauce in Rome.

Over this time there were definitely variations of the recipe and eventually variations with eggs came about. There's a 14th century Spanish cookbook that includes an emulsified egg sauce that is essentially mayonnaise except it includes, of course, garlic and other spices because it was still considered an aioli at the time. From that we can infer that Mayonnaise sort of did exist before the 1750-1850 period but instead of coming up with a new name it was simply called some variation of aioli.

France came up with the name we know it as today and the earliest form of the common 3 ingredients + salt recipe which came about in 1820, prior to that they still added many other flavours to what they now understood was its own sauce uniquely different to aioli.

Mayonaise has a pretty specific ancestry. In 1756, at the early stage of the Seven Years War, the French managed to take Port Mahon in the Baleric Islands from the English. The Duc du Richelieu who was responsible for the victory threw a banquet. He was from northern France, and his cook was used to cream sauces. But on this Mediterranean island there was no milk or cream available, so the cook made up something that was as close to a cream sauce as possible. In honor of the victory, the sauce was dubbed Mahonaise, which evolved to Mayonaise.

This really happened. But, as you say, there's no reason to suppose mixing egg, oil and something like lemon juice could not have happened earlier. It's just that we know the story of this version.