How do we know that Muhammad really existed? Because of all the historians that reported him in their books that are recorded. So lets go to these sources one by one. Years are given in common era.
Urwah ibn Zubayr (d.712): Son of Asma bint Abi Bakr and Zubair ibn alAwwam. He wrote a biography of Muhammad which he subsequently destroyed after the Battle of Harrah. How do we know all this? Through ibn Khallikan (d.1282) and ibn Hajar alAsqalani (d.1449). (Comment: This is not acceptable based on common sense.)
Aban bin Uthman bin Affan (d.723): Son of the Umm Amr bint Jandab and the 3rd Caliph Uthman. He wrote the Maghazi of Muhammad. How do we know that? Why its our good old friend ibn Hajar alAsqalani (d.1449). (Comment: This is not acceptable.)
Wahb ibn Munabbih (d. 725-737): Son of Munabbih ibn Kamil. He wrote Qisas alAnbiya. How do we know that? That’s right, our man ibn Khallikan (d.1282) and ibn Hajar alAsqalani. (Comment: Really, again, another guy not acceptable. His death must be painful or the writers just couldn’t make up their mind.)
ibn Shihab alZuhri (d.741-2): Wrote the Sira of Muhammad. How do we know that? Well now we can rely on someone different this time, namely ibn Sa’d (d.845). (Comment: I don’t find it acceptable.)
ibn Ishaq (d.770): He never wrote the Sira of Muhammad rather his student alBakkai who committed to writing what he had learnt from ibn Ishaq but later ibn Hisham edited the work of alBakkai, more on that below. (So another iffy writer.)
Malik bin Anas (d.795): He wrote alMuwatta which is still in circulation. [Note from this point onwards we have the books of the authors]
Hisham Ibn Al-Kalbi (d.819): He established that Muhammad was from the children of Ishmael and subsequently all the Arabs are the children of Ishmael.
alWaqidi (d. 823): He wrote Kitab alTarikh wa alMaghazi.
Ibn Hisham (d. 835): He wrote the Sira of Muhammad which was actually just an editing od alBakkai’s work. This work survives.
Ibn Sa’d al-Baghdadi (d.845): He wrote Kitab Tabaqat alKubra which contains material on Muhammad and his companions. This work has survived.
Khalifah ibn Khayyat (d.854): There are only two works of his that survive, one is Tabaqat and the other is Tarikh, an 11th century copy was discovered in Rabat, Morroco. He was also the teacher of Bukhari and Ahmad ibn Hanbal.
Ahmad ibn Hanbal (d. 855): He wrote the famous Musnad.
alDarimi (d. 869): He wrote the Sunan alDarimi.
Muhammad alBukhari (d. 870): He wrote Sahih alBukhari, part of Kutub alSittah.
Muslim ibn alHajjaj (d.875): He wrote Sahih Muslim, part of Kutub alSittah.
ibn Majah (d. 887-9): He wrote Sunan ibn Majah, part of Kutub alSittah.
Abu Dawood (d. 889): He wrote Sunan Abu Dawood, part of Kutub alSittah.
Muhammad ibn Isa at-Tirmidhi (d.892): He wrote Jami alTirmidhi, part of Kutub alSittah, amongst other works.
anNasa’i (d.915): He wrote asSunan asSughra, part of Kutub alSittah.
Conclusion: One must bear in mind that Muhammad died in the year 632 of common era and the first three people on the list above were claimed to be historians by people in the 13th century and later. No one who witnessed Muhammad wrote about Muhammad. The fact of the matter is that generally there are 3-7 people in the transmitters of any tradition. Lets keep in mind that this is the time when most people had very low education, infact most people had no education and they believed some of the most laughable things like 360 angels carrying the moon and the sun everyday.
One more thing that needs to be said about this is the fact that the Muslim calender starts right about when the Persian-Byzantine war came to an end with the victory of Byzantine. At that point both the empires were tired making them easy pickings by the two large local factions which were Lakhmid and Ghassanid. Islam will only make sense when historians pay a closer attention to the two Arab tribes.