Humans are referred to with a couple of different words in the Quran. Primary among them are Insan (human) and Naas (people)
Insan
Adam (AS) was created from clay, then Allah blew into him to make him come alive. This is the well-known story of his creation mentioned multiple times in the Quran.
Throughout the Quran, Allah considers this the creation of humanity or "man" (Insan) itself. Insan can be called "human" or "man" or "humanity."
Allah says:
And We did certainly create man out of clay from an altered black mud. (15:26)
This verse is referring to the creation Adam (AS), but notice how Allah attributed it to "man" in general. This is only possible because Adam (AS) was the start of humanity.
Similar verses where the creation of Adam (AS) is referred to as the creation of "man" in general or "humanity" are common.
And certainly did We create man from an extract of clay. (23:12)
Who perfected everything which He created and began the creation of man from clay. (32:7)
He created man from clay like [that of] pottery. (55:14)
Naas
Similarly, Allah attributes "people" (Naas) to the creation of Adam (AS).
First of all, Allah considers people to have been created by one couple of male and female.
Allah says:
O mankind, fear your Lord, who created you from one soul and created from it its mate and dispersed from both of them many men and women. (4:1)
O mankind, indeed We have created you from a male and a female and made you peoples and tribes that you may know one another. (49:13)
You can see that the creation of people is considered to be from one male and one female. This has always been understood as Adam (AS) and his wife. There is no other interpretation of this present.
Secondly, Allah attributes the creation of Adam (AS) from dust to "people." This also indicates that Adam (AS) himself was the start of people in general.
O People, if you should be in doubt about the Resurrection, then [consider that] indeed, We created you from dust (22:5)
Children of Adam
Allah considers all of us the children of Adam in the Quran.
And of His signs is that He created you from dust; then, suddenly you were human beings dispersing [throughout the earth]. (30:20)
And We have certainly created you, [O Mankind], and given you [human] form. Then We said to the angels, "Prostrate to Adam"; so they prostrated, except for Iblees. He was not of those who prostrated. (7:11)
He continuously refers to us with "O Children of Adam" and the clear intent is to indicate that we are all the children of Adam:
O children of Adam, We have bestowed upon you clothing to conceal your private parts and as adornment. But the clothing of righteousness - that is best. That is from the signs of Allah that perhaps they will remember. (7:26)
O children of Adam, if there come to you messengers from among you relating to you My verses, then whoever fears Allah and reforms - there will be no fear concerning them, nor will they grieve. (7:35)
More verses with this phrase: 7:27, 7:31, and 36:60.
Insan and Naas come from Adam
Seeing the many verses above, we can easily figure out that humanity as the Quran refers to it comes from Adam (AS). There was no Insan or human before Adam (AS). If there were any creatures before him, they were not considered human or worthy of consideration.
Adam was created from clay and not from parents
This is very clear in the Quran. Allah says:
Indeed, the example of Jesus to Allah is like that of Adam. He created Him from dust; then He said to him, "Be," and he was. (3:59)
Meaning, Jesus was created without a father just like Adam (AS) was created without any parents.
Adam was a prophet
The definition of prophet is someone who received revelation from Allah. The fact that Adam (AS) received revelation from Allah is very clear in the Quran. Allah says:
Then Adam received from his Lord [some] words, and He accepted his repentance. Indeed, it is He who is the Accepting of repentance, the Merciful. (2:37)
There is no necessity for prophets to be sent to a group of existing people. However, prophets do spread guidance to those who need it. In that sense, Adam (AS) taught his children and descendants. He wasn't sent to a specific pre-existing group. Adam (AS) was not a messenger
The first messenger was Nuh (AS) who was sent to his people.