Did Robin Hood actually exist?

Probably not as a single person — the evidence points instead to a name that became a label, applied to outlaws generally, which then accumulated a legend around it.

The strongest piece of evidence, and it cuts against him. By the thirteenth and fourteenth centuries, "Robinhood" appears in legal records as a nickname for outlaws — court rolls record fugitives given the name, in different places and years. That is the pattern you would expect if the name were already a generic term for a bandit, and it makes identifying "the real one" among them circular.

Candidates have been proposed from those records, and none can be connected to the legend by anything other than the name.

How the legend actually grew:

The earliest surviving ballads date from the fifteenth century, though references to "rhymes of Robin Hood" appear earlier in Piers Plowman, indicating an oral tradition already established.

The early Robin is not what you expect. He is a yeoman, not a dispossessed nobleman; he is violent, and the ballads are bloodier than later versions; his enemies are corrupt clergy and the Sheriff; and he does not obviously rob the rich to give to the poor — that element is a later addition.

Maid Marian and Friar Tuck arrive later, Marian entering partly through May Games rather than the ballad tradition.

The dispossessed noble, robbed of his lands and loyal to King Richard while Prince John usurps, is a post-medieval invention, elaborated substantially in the sixteenth century and fixed in the popular imagination by later novels and film.

Richard the Lionheart's association is not in the early material at all.

Why the story persisted. It encodes a genuinely durable idea — that law and justice can come apart, and that resisting a corrupt authority can be legitimate. That is useful in every century, which is why the character was repeatedly reinvented to suit whoever was telling it.

Locations compete commercially, and neither Nottinghamshire nor Yorkshire has evidence.