Salamun Alaikum,
From a Quranic perspective, 'Messengerships' and 'Prophethoods' are usually applied to the type of ministry that entailed Adam's chosen progeny ‘who came to specific people / nations’ and not to Adam himself.
Therefore, Adam's messengership / prophethood is open to interpretation as he had no predecessor to compare with and was the first 'insaan'. His progeny would also not have existed when he was moved out of the state in which he was in after he ate from the tree. (2:35-38).
Thus it can be argued, that the question is mute in the first place.
However, please read verse 2:37 and note the phrase "fatalaqqa adamu mi rabbihi kalimatin" – ‘Then Adam received from his lord "words"’. Now it is up to the reader to infer what kind of 'words' he would have received given the context, but some kind of words / advice / guidance must be inferred in my humble opinion. This subsequently also infers a role he must have played not only for himself to seek guidance from, but also to pass on these ‘words’ (kalimat) to others in due course.
Furthermore, Prophet Abraham was clearly not the first prophet. If you consult Chapter 6 which lists the 'prophets' in 6:83-89, Prophet Noah is also mentioned in the list who preceded him.
I hope that helps, God willing.
Joseph.