Well, answering this question is as good a reason as any to get up this Saturday morning, so here goes.

The briefest possible answer to your question is: yes, absolutely. Scholars, both working within the Islamic tradition and without have been interested in the historical persona of the Prophet Muhammad basically since Islam and Muslims first appear in the historical record.

Now, there are usually two different ways to interpret the question: "what do we know about the historical Muhammad?":

The first is "did the Prophet Muhammad actually exist?" This one is relatively easy, as the answer is irrevocably "yes". In the same vein that the idea of a "mythical Christ" is now only adhered to be a minority of scholars, there is very little doubt that there was a Prophet named Muhammad who lived in Hijaz in the late 6th/early 7th century.

Sources confirming this are numerous. Very recently, Sean Anthony published Muhammad and the Empires of Faith, in which he seeks to answer exactly this question: "what are the earliest references to Muhammad"? Anthony points out that the first concrete evidence mentioning the Prophet Muhammad by name, surprisingly, comes in the form of numismatics. Specifically, the Zubayrids, who were engaged in a civil war against the Umayyads had a series of struck coins between 685 and 688 AD. These coins represent the first (partial) evidence of the Islamic declaration of faith (šahāda), i.e., "Muhammad is the Prophet of God" (muḥammad rasūl allāh).

The numismatic evidence is further supported by epigraphic material from the middle of the 7th century onwards. During this time, the character of Arabian epigraphy changes radically: inscriptions become explicitly religious and parallel phrases also found in the Qur'ān, and perhaps more importantly, we also start finding references to the hijri calendar. In Islam, the year "1" begins with Muhammad's exile to Yathrib, which later came to be known as Medina. A short inscription west of Madina was written by one Salamah, who states that he wrote his inscription in the year 23.

This is the earliest evidence of the usage of the hijri calendar and may very well have been written by one of Muhammad's contemporaries. Secondly, it shows that within three decades, the hijra had become such an important event that it led to adoption of an entirely new calendar.

Beyond the epigraphic sources from this period, there are also relatively early references in non-Muslim documentary sources from this time. An earlier post already mentioned Shoemaker's recent A Prophet Has Appeared (2021). The first text that Shoemaker mentions is the relatively famous Teaching of Jacob the Newly Baptized, which dates to 632 AD. This text contains the phrase "the Prophet who has appeared with the Saracens". The exact interpretation of this line ("Prophet?", "Saracens?") is of course somewhat controversial, but it almost certainly refers to Muhammad. A later fragmentary text in Syriac (also mentioned by Shoemaker) contains what appears to be the first mention of the named Muhammad (Mwḥmd), whose followers are said to have pillaged their way through Syria. This text is dated to 636 AD.

And of course, beyond the numismatic, epigraphic, and non-Muslim documentary sources there is a vast wealth of material written and transmitted by Muslims. Perhaps the very earliest Muslim texts pertaining to the Prophet's life are a series of letters from ʿUrwah b. al-Zubayr to the Caliph Abd al-Malik and his son al-Walīd. The events mentioned in these letters are not arranged chronologically, but, when rearranged, leaves us with a general outline of the Prophet's life beginning with the first revelations and ending with the conquest of Mecca. These letters are preserved in various traditions ranging back to the end of the 8th and the beginning of the 9th century, and there is little doubt that the correspondence between ʿUrwah and Abd al-Malik was, in fact, genuine.

In the centuries following, Muslim scholarship on the Prophet's life became more elaborate. The first full-length biography of the Prophet is known as al-sīra al-nabawiyya (often simply known as the sīra, "journey; biography", which itself is a redaction of an earlier work by Ibn Isḥāq, which is now unfortunately lost. According to the Islamic tradition, the Prophet died in the year 632 AD and Ibn Hišām died in 833. Now, a critical historian should ask whether it's possible that Ibn Hišām (or his informers) simply "made everything up". In retrospect, this seems extremely unlikely. As mentioned before, ʿUrwah's letters provide us with a general outline of the Prophet's life and none of the later Islamic period biographies paint a radically different picture of his life.

Lastly, it is worth mentioning that there is a tendency to treat medieval Muslim scholarship overly critically. While it is certainly true that Muslim scholars were working in a different ideological framework, they were not uncritical and had developed a rather sophisticated system of determining whether sources and informants were trustworthy or not. Although this is system is not without potential flaws, it is important keeping an open mind.

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Bibliography

Anthony, Sean W. 2020. Muhammad and the Empires of Faith: The Making of the Prophet of Islam. Oakland, California: University of California Press.

Ibn Isḥāq, Muḥammad. 2001. The Life of Muhammad: A Translation of Isḥāq’s Sīrat Rasūl Allāh. edited by M. ʿAbd al-Malik Ibn Hišām. Karachi ; New York: Oxford University Press.

Hoyland, Robert. 1997. Seeing Islam as Others Saw It - A Survey and Evaluation of Christian, Jewish, and Zoroastrian Writings on Early Islam. Princeton: Darwin Press.

Shoemaker, Stephen J. 2021. A Prophet Has Appeared: The Rise of Islam through Christian and Jewish Eyes: A Sourcebook. Oakland, California: University of California Press.

To my knowledge, one of the best and also least speculative work on the topic is by Shoemaker: The death of a prophet.

The first part of the book discusses the contemporary historical sources that mentions Muhammad. For example a priest from Palestinian region mentions an Arab king named Muhammad that brought together the tribes and started moving north.

It's been a while since I have read the book but the author goes into details for each source. Of course you should expect less details on his life more you like to keep your criteria of sources rigorous.

The one main point he is making that according to these sources, it seems like Muhammad lived a few years longer than what regular Islamic sources claim and he was part of the Islamic conquest of the Jordan/Palestinian region (at least southern part). And he died there, not in Madina.this seems like a small detail but it has implications. He discusses those implications.

Then in the rest of the book he argues that Islam/muhammad was at the beginning preaching an impending apocalypse. But that apocalypse did not happen. As a result, believers had to modify their stance and understanding of the religion accordingly.

It is a really good book for anyone seriously interested in the topic. It is less speculative in the sense of resources. So it is not exactly like Tom Holland's book, shadow of the sword. It also exposes reader to earlier studies of Quran and Islam in the west, especially german academia.

edit: One more thing the book does is to also talk about islamic sources. Instead of directly dismissing them, it talks about how the content of hadith(sayings of prophet)/siyar(life of the prophet) depend on the alleged quality of chain of transmission. Some hadith are just too perfect and convenient in terms of content and the chain of transmission. This actually raises more suspicion according to the scholars who uses the certain approach mentioned in the book. And then he looks at the hadith/siyar that talks about prophet's death and shows how it evolved over time. Earliest sources of siyar are much less detailed and have different content compared to the ones written later.