We're never told anything explicit about Gildor's date of birth, but he tells Frodo 'We are Exiles' (The Fellowship of the Ring I 3). Those words seem to imply that Gildor was among the Noldor who followed Fëanor out of Aman after the Darkening of Valinor.

Gildor claims to belong to the House of Finrod, but at the time that passage was written, the name 'Finrod' applied to the character later established as 'Finarfin'. On that reading, Gildor actually belonged to the House of Finarfin (but Tolkien chose not to amend the text after the change of name, so perhaps 'House of Finrod' was intended to stand).