There’s an article about the history of the Papal tiara.
Popes since ancient times had worn some sort of head covering. By the 9th century it would appear that this took the form of a helmet-shaped white head-cap. Pope Gregory the Great (r. 590-604) is shown in contemporary artwork wearing such a headpiece. When exactly it developed its first lower tiara is unclear, though the Catholic Encyclopaedia speculates that it was in or around the 10th century, perhaps to distinguish the ceremonial papal head covering from the ecclesiastical one, the Mitre, which appeared around this era. The first explicit mention of the word tiara associated with the papacy appears in the account of the life of Pope Paschal II (r1099-1118) in the Liber Pontificalis.
A decorated circlet or ornamental band which may be the origins of the first tier of the tiara, is shown on coins of Pope Sergius III (r. 904-911) and Pope Benedict VII (r. 974-983)
So-- it looks like it started off, perhaps, in a tiara-shape-- a circlet or an ornamental band-- around a tall helmet –
before it evolved into a more complicated shape, like when you think of the Renaissance Popes, but which extended into the 20th c.