Muhammad is a historical figure in a way that is not seriously disputed. The precise reconstruction of his life is a different matter, and the source problem is specific.
The Quran is the earliest material. It is understood by Muslims as revelation received between roughly 610 and his death in 632, and the standard account has it collected under the caliph Uthman within about twenty years. Manuscript evidence supports a very early fixation of the text: the Birmingham folios and the Sanaa palimpsest lower text have been radiocarbon dated to the seventh century, and while radiocarbon dates parchment rather than ink, the results sit comfortably with the traditional account. But the Quran is not a biography. It alludes to events without narrating them and names Muhammad only four times.
Everything narrative comes from the sira and hadith literature, and the gap is the issue. Ibn Ishaq wrote the foundational biography around 767, more than a century after the death, and even that survives only in the later recension of Ibn Hisham, who says openly that he omitted material. The great hadith collections of al-Bukhari and Muslim are ninth century. These traditions come with chains of transmitters, and Muslim scholarship developed an elaborate and serious science for evaluating those chains.
Western scholarship has ranged from broadly accepting the traditional framework with caution to radical scepticism about all of it. The sceptical extreme of the 1970s has receded, partly because of the manuscript evidence. The mainstream position now grants the outline and treats the detail as needing case-by-case argument.