As @Bach has already mentioned in comments, accepting the offer given by Allah is a manifestation of the humankind already having at least a level of free will. Not only humankind, but also those who refuse to accept the offer have at least a level of free will.
إِنَّا عَرَضْنَا الْأَمَانَةَ عَلَى السَّمَاوَاتِ وَالْأَرْضِ
وَالْجِبَالِ فَأَبَيْنَ أَن يَحْمِلْنَهَا وَأَشْفَقْنَ مِنْهَا
وَحَمَلَهَا الْإِنسَانُ ۖ إِنَّهُ كَانَ ظَلُومًا جَهُولًا
Indeed, we offered the Trust to the heavens and the earth and the
mountains, and they declined to bear it and feared it; but man
[undertook to] bear it. Indeed, he was unjust and ignorant.
So, this is not the place for Allah to give the humankind the free will. Indeed, in the same verse, Allah has announced what was the driving force to accept what the other creatures declined to accept. The man accepted it out of ignorance and unjust, while the others refused to accept it out of fear. The state of the man which led it to accept the offer is also explained in other verses, that:
إِنَّ الْإِنسَانَ لِرَبِّهِ لَكَنُودٌ ﴿٦﴾ وَإِنَّهُ عَلَىٰ ذَٰلِكَ
لَشَهِيدٌ ﴿٧﴾ وَإِنَّهُ لِحُبِّ الْخَيْرِ لَشَدِيدٌ ﴿٨﴾
Indeed mankind, to his Lord, is ungrateful. (6) And indeed, he is to
that a witness. (7) And indeed he is, in love of wealth, intense. (8)
This intense love of wealth led him to accept such a great offer that the heavens and the earth had fear from its acceptance. According to Shia Ahadeeth, the great offer is something that Praying Allah (صلوٰة) is a major manifestation of it:
"وَاسْتَعِينُوا بِالصَّبْرِ وَ الصَّلَاةِ ۚ وَ إِنَّهَا
لَكَبِيرَةٌ إِلَّا عَلَى الْخَاشِعِينَ ﴿٤٥﴾ ".
And seek help through patience and prayer, and indeed, the
latter being difficult except for the humbly submissive [to Allah]
(45)
There are a lot in Ahadeeth and the saying of the scholars of Shia about this verse, but this much should suffice in response to your question.
About free will also there are tons of arguments, but only mention that the free will, as much as it is free will, does not belong to human kind only. Angels, animals, plants, and even stones and those which we consider as not alive, they all have free will to some extent. Even we have Ahadeeth that they will resurrect at the Day. For example have you seen these verses:
وَمَا مِن دَابَّةٍ فِي الْأَرْضِ وَلَا طَائِرٍ يَطِيرُ بِجَنَاحَيْهِ
إِلَّا أُمَمٌ أَمْثَالُكُم ۚ مَّا فَرَّطْنَا فِي الْكِتَابِ مِن شَيْءٍ
ۚ ثُمَّ إِلَىٰ رَبِّهِمْ يُحْشَرُونَ
And there is no creature on [or within] the earth or bird that flies
with its wings except [that they are] communities like you. We have
not neglected in the Register a thing. Then unto their Lord they
will be gathered.
أَلَمْ تَرَ أَنَّ اللَّـهَ يَسْجُدُ لَهُ مَن فِي السَّمَاوَاتِ وَمَن
فِي الْأَرْضِ وَالشَّمْسُ وَالْقَمَرُ وَالنُّجُومُ وَالْجِبَالُ
وَالشَّجَرُ وَالدَّوَابُّ وَكَثِيرٌ مِّنَ النَّاسِ ۖ وَكَثِيرٌ حَقَّ
عَلَيْهِ الْعَذَابُ ۗ وَمَن يُهِنِ اللَّـهُ فَمَا لَهُ مِن مُّكْرِمٍ ۚ
إِنَّ اللَّـهَ يَفْعَلُ مَا يَشَاءُ ۩ ﴿١٨﴾
Do you not see that to Allah prostrates whoever is in the heavens and
whoever is on the earth and the sun, the moon, the stars, the
mountains, the trees, the moving creatures and many of the people? But
upon many the punishment has been justified. And he whom Allah
humiliates - for him there is no bestower of honor. Indeed, Allah does
what He wills. (18)
تُسَبِّحُ لَهُ السَّمَاوَاتُ السَّبْعُ وَالْأَرْضُ وَمَن فِيهِنَّ ۚ
وَإِن مِّن شَيْءٍ إِلَّا يُسَبِّحُ بِحَمْدِهِ وَلَـٰكِن لَّا
تَفْقَهُونَ تَسْبِيحَهُمْ ۗ إِنَّهُ كَانَ حَلِيمًا غَفُورًا
The seven heavens and the earth and whatever is in them exalt Him. And
there is not a thing except that it exalts [Allah] by His praise, but
you do not understand their [way of] exalting. Indeed, He is ever
Forbearing and Forgiving. (44)
These are all through free will ...
