All the known trustworthy facts actually reject the idea that Muhammad () even had the slightest knowledge about prophethood (and its burden) nor Allah's message before being appointed and even at the moment he was appointed he was in total fear for what he has seen and experienced as the first ahadith in Sahih al-Bukhari (and elsewhere which were narrated via ibn Shihaab az-Zuhri ابن شهاب الزهري and on the authority of 'Aishah: note that some of these narrations suggest that the prophet thought about suicide) show.
And even if we assume that he () somehow knew about it, he certainly was not prepared for what he will experience. Note that no reliable source actually confirms that Muhammad was taught anything related to religion and the qur'an in many verses tries to deny the possible input from Christian or Jewish preachers, monks, rabbi's or priests. And those sources saying that people expected him to be a prophet appear in first place in the works of historians who where known to be very lenient in their choice of sources and narrators. Note that these historians after quoting that Muhammad was close to a-Shaam in his childhood with his uncle and warned from going there either because of the Romans or Jews (based on different narrations) apparently ignored that he nevertheless is known to have been there once again in as a young man when he was trading for his later wife Khadijah. As if he didn't care about this warning!
But there are still a couple of events that might have had lead him to the conclusion that he might be someone special. Depending on the circumstances and to how deep he () discussed them with others before his appointment.
It seems that none of the prophets knew about their appointment
The qur'an actually denies this not only for our prophet (), but one could conclude from the few statements that it is a general denial.
For example when Allah speaks about the appointment of Musa/Moses () it says:
And has the story of Moses reached you? - (9)
When he saw a fire and said to his family, "Stay here; indeed, I have perceived a fire; perhaps I can bring you a torch or find at the fire some guidance." (10)
And when he came to it, he was called, "O Moses, (11)
Indeed, I am your Lord, so remove your sandals. Indeed, you are in the sacred valley of Tuwa. (12)... (20:9-12 etc.)
Which shows that even Moses () was not aware that he might be appointed as a prophet, even if he had been saved several times and had -after all we know about him compared to Muhammad ()- more information about Allah, the religion, the Unity of God (28:14-17) and he knew about Yusuf () who was appointed earlier (40:34) and even has met Prophet Sho'aib according to some scholarly views and interpretations of the wise man he met in Madian.
As Allah tells us:
He gives wisdom to whom He wills, and whoever has been given wisdom has certainly been given much good. And none will remember except those of understanding. (2:269)
The wisdom Allah gives us usually is a revelation which also requires a prophet or messenger who receives it and teaches it to his people.
And when a sign comes to them, they say, "Never will we believe until we are given like that which was given to the messengers of Allah ." Allah is most knowing of where He places His message. There will afflict those who committed crimes debasement before Allah and severe punishment for what they used to conspire.(6:124)
The bold statement in this verse might be understood literally or referring to Prophets and Messengers, especially as the disbelievers or hypocrites wanted to get the same gifts they've got from Allah!
Allah chooses from the angels messengers and from the people. Indeed, Allah is Hearing and Seeing. (22:75)
So the final choice whether a person will be a prophet or not is by Allah. Yes HE may have chosen some prophets and messengers from one family, but even there HE made a choice and picked a certain individual (or more) from the offspring etc.
However Allah may decide to agree to support a messenger with a person of his choice as HE did with Musa () (See for example 20:29-30 or 28:34). One may discuss whether this was a divine inspiration or really a proposal idea Musa himself came with and if so whether or not he already has proposed or discussed this with Harun () earlier!
What the qur'an tells us about Muhammad
When speaking about Muhammad (), Allah the Almighty presents him as the unlettered prophet النبي الأمي as it is the case in (7:157) and (7:158): unlettered might refer to a condition of not having learnt to read and write, but it also may refer to a person who simply lacks knowledge about a matter.
And further more the qur'an shows that Muhammad was not aware of any knowledge about revelation before his appointment saying:
And thus We have revealed to you an inspiration of Our command. You did not know what is the Book or [what is] faith, but We have made it a light by which We guide whom We will of Our servants. And indeed, [O Muhammad], you guide to a straight path - (42:52)
So how would a person that never heard or knew about all of these even think of being a (or the) chosen prophet and messenger?
Finally note that the qur'an also tells us that Allah the Almighty even if HE realized the du'a of Ibrahim () for the Arab nation (asking for a prophet from among them):
Our Lord, and send among them a messenger from themselves who will recite to them Your verses and teach them the Book and wisdom and purify them. Indeed, You are the Exalted in Might, the Wise." (2:129)
He didn't follow the order of gifts when appointing Muhammad ():
It is He who has sent among the unlettered a Messenger from themselves reciting to them His verses and purifying them and teaching them the Book and wisdom - although they were before in clear error - (62:2)
So assuming Muhammad () was aware of this du'a how would he identify himself as this person before getting a revelation and starting to spread his message?
Maybe relevant: discussion of the veracity of the meeting between Muhammad and a monk during his childhood: At age of 12 One of Christian father told to our prophet that you will become as a prophet. Who is that father?
A human forgets
It is even said in Arabic that humans have been called "insaan إنسان" because they do forget ( nisyaan نسيان) very much:
قيل أنه سُمي إنسانا لكثرة نسيانه
So forgetting is part of our human nature!
When Allah speaks about Himself He says:
... And never is your Lord forgetful - (19:64)
… My Lord neither errs nor forgets (20:52)
While Allah describes humans (including prophets) saying:
ربنا لا تؤاخذنا إن نسينا أو أخطأنا
… "Our Lord, do not impose blame upon us if we have forgotten or erred. …" (2:286)
And We had already taken a promise from Adam before, but he forgot; and We found not in him determination. (20:115)
[ Allah ] will say, "Thus did Our signs come to you, and you forgot them; and thus will you this Day be forgotten." (20:126)
See also the verses (32:14), (45:34).
And He even addressed Muhammad () directly reminding him saying:
Except [when adding], "If Allah wills." And remember your Lord when you forget [it] and say, "Perhaps my Lord will guide me to what is nearer than this to right conduct." (18:24)
All this shows that all of us do forget either unintentionally or out of fear as we don't want to recall something that happened earlier in our life, so we keep it hidden somewhere in our mind until we don't even recall it any more. This includes the prophet Muhammad () who might have witnessed some miracles in his childhood or youth, but considered some of them as something frightening and forgot about them or other events until he was recalled later. But Allah knows best!
The most important for all of us is that we should always keep our faith in Allah and always have Him in mind as else:
And be not like those who forgot Allah , so He made them forget themselves. Those are the defiantly disobedient. (59:19).
My conclusion is that at the time of his appointment Muhammad () was not aware neither of prophethood nor of any miracle that happend to him in his early years. This either means he forgot about them or Allah made him forget as he himself said:
"I forget or I am made to forget so that I may establish the sunna." (Al-Muwatta')
This seems to me the closest interpretation of all sources and Allah knows best!