Qur'an 28:15 describes an incident in which Prophet Musa killed an Egyptian man (unintentionally; see IslamWeb), and the next verse (Qur'an 28:16) describes Allah forgiving him. Afterwards, Prophet Musa was called to prophethood:
[Moses] said, "I did it, then, while I was of those astray. So I fled from you when I feared you. Then my Lord granted me wisdom and prophethood and appointed me [as one] of the messengers.
It's usual to consider Prophet Muhammad as becoming a prophet (rather than born a prophet). Nevertheless, even before prophethood, Muhammad is described as a man with exemplary character. Some examples of this in fatawa are:
He was known before becoming a Prophet as a truthful and honest person, although the community where he lived was a society of ignorance.
But nothing of the sort happened, rather before his Prophethood they used to call him al-Saadiq (the honest one) and al-Ameen (the trustworthy one).
Moreover, Prophet Muhammad acted shocked after the first revelation:
Then Allah's Messenger returned with that experience; and the muscles between his neck and shoulders were trembling till he came upon Khadija (his wife) and said, "Cover me!"
If Prophet Muhammad was already a prophet beforehand, then it seems he was unaware of it.
It seems Prophet Adam was not even born (but created), although it's reasonable to expect he was created a prophet.
It's reasonable to think Prophet Isa was born a prophet, given he talked from the cradle (Qur'an 19:30).