It is not that Quran is trusted because Mohammad (PBUH) is trusted.
It is the reverse!
The main miracle of the Mohammad (PBUH) is Quran.
The prophethood of Mohammad (PBUH) is accepted
because Quran is a miracle, not vice versa.
The claim that Mohammad (PBUH) made up Quran by himself
was made even during his time, and
it is mentioned in Quran.
It is not a new claim,
according to Quran this was used also against previous prophets.
E.g. in verse 23:38 it states that
previous nations made the same claim against their prophets:
إِنْ هُوَ إِلَّا رَجُلٌ افْتَرَىٰ عَلَى اللَّهِ كَذِبًا وَمَا نَحْنُ لَهُ بِمُؤْمِنِينَ
If he is but a man who has fabricated a lie on God and we are not believers to him.
Quran clearly makes the claim in several places that
it is not the work of a man and
in fact challenges those who do not accept its authenticity
to produce something similar.
E.g. in verse 2:23 it says:
وَإِن كُنتُمْ فِي رَيْبٍ مِّمَّا نَزَّلْنَا عَلَىٰ عَبْدِنَا فَأْتُوا بِسُورَةٍ مِّن مِّثْلِهِ وَادْعُوا شُهَدَاءَكُم مِّن دُونِ اللَّهِ إِن كُنتُمْ صَادِقِينَ * فَإِن لَّمْ تَفْعَلُوا وَلَن تَفْعَلُوا فَاتَّقُوا النَّارَ الَّتِي وَقُودُهَا النَّاسُ وَالْحِجَارَةُ ۖ أُعِدَّتْ لِلْكَافِرِينَ
And if you are in doubt regarding what we have sent down to our servant
then come up with a sura like it and
call upon your witnesses other than God if you are honest.
Thus if you do not, and surely you cannot,
then be mindful of the fire whose fuel are people and stones
[which is] promised for disbelievers.
Or in verse 17:88:
قُل لَّئِنِ اجْتَمَعَتِ الْإِنسُ وَالْجِنُّ عَلَىٰ أَن يَأْتُوا بِمِثْلِ هَٰذَا الْقُرْآنِ لَا يَأْتُونَ بِمِثْلِهِ وَلَوْ كَانَ بَعْضُهُمْ لِبَعْضٍ ظَهِيرًا
Say: even if the mankind and the genies were to gather together
to come up with the like of this Quran,
they would not come up with the like of it,
even if some of them helped some other.
A lot has been written about why Quran is a miracle.
One of the main ones I think is stated in verse 28:49:
قُلْ فَأْتُوا بِكِتَابٍ مِّنْ عِندِ اللَّهِ هُوَ أَهْدَىٰ مِنْهُمَا أَتَّبِعْهُ إِن كُنتُمْ صَادِقِينَ
Say: come up with a book from God which guides better than them
[so] I will follow it, if you are honest.
Here them refers to Quran and Torah.
Also there is a metaphor in verse 13:31 about Quran:
وَلَوْ أَنَّ قُرْآنًا سُيِّرَتْ بِهِ الْجِبَالُ أَوْ قُطِّعَتْ بِهِ الْأَرْضُ أَوْ كُلِّمَ بِهِ الْمَوْتَىٰ ۗ بَل لِّلَّهِ الْأَمْرُ جَمِيعًا ۗ أَفَلَمْ يَيْأَسِ الَّذِينَ آمَنُوا أَن لَّوْ يَشَاءُ اللَّهُ لَهَدَى النَّاسَ جَمِيعًا ۗ وَلَا يَزَالُ الَّذِينَ كَفَرُوا تُصِيبُهُم بِمَا صَنَعُوا قَارِعَةٌ أَوْ تَحُلُّ قَرِيبًا مِّن دَارِهِمْ حَتَّىٰ يَأْتِيَ وَعْدُ اللَّهِ ۚ إِنَّ اللَّهَ لَا يُخْلِفُ الْمِيعَادَ
If indeed there was a Quran that mountains were moved with it, or
the earth were cloven asunder with it, or
the dead were made to speak with it,
[this is it],
but [only] for God is the command, all of it.
So have't those who believe become despaired that
if God wanted he surely could guide people, all of them?
And those who disbelieve do not cease to be struck,
for what they have done, by calamity, or
it will descend near their home,
until there comes the promise of God.
Indeed God does not break promise.
Now, since Quran is a book,
it is not a miracle restricted to a particular location or time.
It is a timeless and location-less miracle that is
presented to us.
But it is not that anyone who sees a miracle
would accept it.
You mentioned Moses (PBUH),
the Pharaoh and his people saw the miracles done by him,
but they still rejected them and called him a magician.