It’s circumstantial, but I think there’s a good degree of evidence looking at space, time, and text. I’m using historical-critical readings of the Quran and Hadith to make the claim.
First, Chalcedon took place in 451 AD, and Muhammad’s first “revelation” took place in 610 AD. In that 161 years, a lot happened. The non-Chalcedonian churches split off from the Byzo-Romans in Constantinople, and the Christological conflicts between them seem to prefigure the Quran’s and Hadith’s railings against Jesus being God. In particular, Nestorian Christians (dyophysites) in Syria condemned the Jacobite (miaphysite) Christian view that implied that there was one nature in Christ (like water and wine in a cup).
Caravans that traded with Meccans traveled through Syria, establishing a route by which news and stories of the Christian world could influence Muhammad (who was a trader).
There’s evidence in the Quran of a particular hostility toward Jacobite/miaphysite Christians. In particular, the description of the
Marib Dam’s failure in the 570s, resulting in the displacement of thousands of refugees that flowed north from Yemen and the destruction of the agricultural bounty for which the region had been long famed (Saba = Sheba, mentioned in the Old Testament). This was a catastrophe that left an indelible mark on the people of the region. Islam interpreted it as evidence of God’s wrath against the “turning away” of the people of the region. The region had been recently conquered by the Himyarites, from Ethiopia who held both miaphysite and heavily Judaic beliefs. The disaster left a nice big target on miaphysite beliefs.
In Sura 34 (Saba), we see the failure of the dam blamed on the “turning away” of the people of Saba:
So by this theory, Muhammad was participating in the Christological conflicts among the non-Chalcedonian Christians of his region of the world. Notably, the Hijaz lies close to the borders of miaphysite (e.g., Ghassanids) and dyophysite (e.g., Syrian) Christians.
There is other evidence that Muhammad was participating in Christian debates of his day. Notably, Sura 5 (the feast) includes an incongruous reference to what appears to be the Eucharist, with Allah sending down a feast from Heaven. Even the Quran says that failing to believe in this “feast” will result in unparalleled punishment against the disbeliever:
To me, there can be very little doubt that these words are taken almost verbatim (given translation and later Muslim redaction) from John 6, with a crowd that follows Jesus after the feeding of the five thousand, and Jesus declaring himself to be the bread come down from heaven, saying that unless you eat/drink of him, “you shall have no life within you.” To me, the parallels are undeniable.
There are other Christian apocrypha and folk stories in the Quran. The Quran includes the story of young Jesus blowing life into clay birds, a story found in the apocryphal Infancy Gospel of Thomas. The Quran includes the story of the
Seven Sleepers, a story first told by the Syrian bishop, Jacob of Saraug (c. 450-521). All these emphases suggest that Muhammad was drawing from a rich tradition of Christian culture.
I can’t prove for sure that Muhammad thought he was participating in Christian conflicts, but do know that Uthman burned all extant copies of the Quran that he hadn’t had redacted and edited to reflect his own conception of what Islam was supposed to be.