The following excerpt is my personal interpretation as I was not able to find to find a scholarly material to support it:
Regarding the statements in the Quran:
Indeed, Allah chose Adam and Noah and the family of Abraham and the family of ‘Imran over the worlds – (Quran 3:33)
Those were the ones upon whom Allah bestowed favor from among the prophets of the descendants of Adam and of those We carried [in the ship] with Noah, and of the descendants of Abraham and Israel, and of those whom We guided and chose. When the verses of the Most Merciful were recited to them, they fell in prostration and weeping. (Quran 19:58)
‘As has been pointed out by Siraj Islam, the above verses are referring to a plurality of people and not a ‘particular’ person. Thus Adam represents the people of Adam; and Noah, the people of Noah. This is obvious from the following mention of ‘the family of Abraham’ and ‘the family of Imran’; as well as the second verse (19:58) which mentions ‘descendants of Adam’ , ‘of those We carried [in the ship] with Noah’, descendants of Abraham and Israel.’ (Lamp of Islam)
However, I differ slightly on the possible understandings of the concept.
One way to interpret these verses is to say that they are a reference to Mankind (Adam represents Mankind), and the following mentioned prophets are included in this general category.
The other possible interpretation according to me is that the names mentioned in these verses are archetypes. The archetype ‘Adam’ is both a proper name and at the same time represents the ‘people of Adam’ or those people this verse connects him to. This is a logical conclusion since the next sentence states ‘and of those We carried [in the ship] with Noah‘, in other words, people associated with Noah; as well as the statement frequently used by the Quran: ‘Children of Adam’. Here again, the whole human race is meant even if Adam specifically was the first prophet, a member of the human race. Various scholars have used this phrase (the children of Adam) in this way.
According to Ghulam Ahmad Pervez:
‘It is believed that Adam, supposedly the first man created by Allah, (whose story is narrated in the Quran regarding his exit from Jannah) was the first Rasool. This is not supported by any verse of the Holy Quran, neither is the name of Eve (Hawwa) mentioned in the Quran. The story is narrated in a symbolic form and does not pertain to a particular person or a couple; in fact this is the story of mankind and Adam is its representative. The word Adam occurs 25 times in the Quran and only in one place (3:32) it appears that Adam was also the name of a chosen person.’ (Exposition of the Quran, p. 1141.)
Thus we can conclude from this that ‘Adam’ is both a a prototype which represents humanity and also a ‘proper name’ for the first prophet Adam (peace be upon him).
The distinction is difficult because the story of Adam is allegorized. The history of the early people is connected to the first prophet in an extremely complicated way.
However, as Muslims, we must keep in mind that belief in all the messengers and prophets is binding on us. We should not reject a single prophet unless we have legitimate proof that such a person was not a prophet. That Adam was the first prophet is logical. If humanity developed from the animal world; it is clear that when they reached maturity (in evolution), they would not be able to coexist without Allah’s guidance. It is only logical thus that the first prophet’s story is linked to humanity’s beginnings.
Another line of logic can help us understand that Adam was indeed a real person: the Hadith literature. It should be kept in mind that the narrations in the hadith literature of humanity’s beginnings are all allegories describing a particular concept. As explained by Dr. Jonathan Brown (link), a particular ‘mystical’ narration may be describing a concept or conveying a particular message, even though it is in a very allegorical form. Thus, things like ‘woman created from Adam’s rib’ is not to be taken literally. Another example is Adam’s 60 cubits tall height. The hadith saying this are not to be taken literally; Adam’s 60 cubit tall height might just be talking about Adam’s innocence or tallness in terms of spirituality (that Adam was an extremely guided person). And humanity decreasing in size since Adam’s day might be talking about humanity’s spiritual regression over time. This interpretation is consistent with other hadiths that literally describe this concept and various Quranic verses as well. Indeed, the prophet could’ve received these revelations in particular pictorial forms, not as literal and scientific facts. The foregoing is obviously only a conjecture by me, but this idea I feel carries a lot of logical weight.
Once this idea is understood about the hadith literature, we can turn to the literal narrations where Adam is described as a real person. For example the hadith quoted by Ibn Kathir (Tafsir Ibn Kathir surah 2 pg. 116):
“The believers will gather on the Day of
Resurrection and will say, `We should seek a
means of intercession with our Lord.
They will go to Adam and say, `O Adam! You are
the father of all mankind, Allah created you with
His Own Hand, ordered the angels to prostrate for
you and taught you the names of everything. Will
you not intercede for us with your Lord, so that
he relieve us from this gathering place.’ “
Everyone knows that the believers make this request to all the prophets mentioned in the Quran until they finally reach Muhammad; so Adam here must be referring to a real person!
Brown, Jonathan. (2016). https://www.youtube.com/watch?v=SH3JPQUSUr4&feature=emb_title
Kathir, Ibn. Tafsir Ibn Kathir. (vo. 1 p. 116). https://ia803208.us.archive.org/22/items/TafseerIbnKathirenglish114SurahsComplete/002BaqarahI.pdf
Islam, Siraj. (2015). Lamp of Islam. https://lampofislam.wordpress.com/2015/06/30/is-adam-a-prophet/
Pervez, Ahmad (2010). Exposition of the Quran. (p. 1141). http://www.islamicweblibrary.com/wp-content/uploads/2020/04/ExpositionOfHollyQuran.pdf