There are a few accounts from the first couple centuries of Islam of this new movement from outside perspectives, although they are not as numerous as one would like or perhaps even expect. It's very late where I am right now, so I can update this tomorrow if there isn't a better answer by then, but I will link a few books that collect and discuss these sources below. I'll just say right now though that the formative years of Islam is a very active area of research, and there are a lot of debates about what exactly these sources are telling us.

Stephen Shoemaker, A Prophet Has Appeared: The Rise of Islam through Christian and Jewish Eyes

Michael Penn, When Christians First Met Muslims A Sourcebook of the Earliest Syriac Writings on Islam

Robert G. Hoyland, Seeing Islam As Others Saw It: A Survey and Evaluation of Christian, Jewish and Zoroastrian Writings on Early Islam

Several of these books engage with Fred Donner's book, Muhammad and the Believers, an influential account of Muhammad's movement as broadly monotheist and not a distinct "religion" at its origin. Of note also is the controversial and rather difficult to acquire Hagarism by Patricia Crone and Michael Cook, which really reignited the debate about Islamic origins a half century ago. The authors wrote it as grad students iirc, and I think Cook basically disavows it at this point lol.