Do you know of any Syriac sources which mirror the context of the manuscripts few verses?
This book is a good introduction to the late-antique context or some of the material.
https://serdargunes.files.wordpress...-historical-context-gabriel-said-reynolds.pdf
Part of the manuscript is Surat al-Kahf which has similarities with Syriac Alexander Legend and the & 7 Sleepers of Ephesus. The parts that relate to Dhul Qarnayan (Alexander) are not in this manuscript and are often considered, in the Islamic tradition, to have been later revelations. Chapters 5 and 8 of the above document relate to this, 8 is especially interesting as the Alexander Legend
Al-Kahf contains 3 stories, about Moses, the sleepers, and Dhul Qarnayan, and in the Islamic tradition theses were said to be revealed in response to questions/challenges from 'people of the book'.
There is plenty on the Quran that links to its emergence in the multicultural and religiously heterogenous Middle East of late antiquity. As well as the previously mentioned myths that are alluded to there are also examples related to the Infancy Gospel of Thomas, the Protevangeleum of James and Gospel of pseudo-Matthew that relate to Mary. The 2nd part in the manuscript relates to Surat Maryam, discussed in Ch 5 of the link I provided above.
Another couple of articles about early Islam
http://chaserobinson.net/files/2014/03/HeilgeschichteMarch2014.pdf
https://www.opendemocracy.net/faith-europe_islam/mohammed_3866.jsp
Also various articles about early Islam here, some of which start getting a bit more technical/specific:
https://nyu.academia.edu/RobertHoyland (Robert Hoyland's books Seeing Islam as others saw it and the Arab conquests are excellent also)
https://slu.academia.edu/CarlosSegovia
A good book that shows Jewish/Christian conflict in the Hijaz in the years leading up to the founding of Islam is The Throne of Adulis by Glen Bowersock.
It is worth noting that this is an area of study where there are, unsurprisingly, many disagreements. It is also an area where, due to the time passed and the lack of contemporary physical evidence, it is difficult to make hypotheses that are not in some way tentative/speculative. Even among academics, never mind religious believers, there are often counterarguments to many points raised. If you like history though, it's a very interesting time period.
Even if someone accepts that the Quran is the perfect word of God, it is pretty clear that God chose to reveal a religion that exactly fits the time and place it was revealed in, but I suppose this is unsurprising.