How do we know the Buddha existed and his teachings are authentic?

According to the book The Authenticity of the Early Buddhist Texts:

1. there is a body of Early Buddhist Texts (EBTs), which is clearly distinguishable from all other Buddhist scripture;
2. these texts originated from a single historical personality, the Buddha

The book’s main conclusion is:

… that the Early Buddhist Texts originated in the lifetime of the Buddha or a little later, because they were, in the main, spoken by the Buddha and his contemporary disciples. This is the most simple, natural, and reasonable explanation for the evidence.

Our argument covers two main areas:

• The grounds for distinguishing the Early Buddhist Texts (EBTs) from later Buddhist literature;
• The evidence that the EBTs stem from close to the Buddha’s lifetime, and that they were generally spoken by the historical Buddha.

However, it is also true (from the book) that:

… the texts bear all the marks of redaction and editing, and that they have been optimised for the oral tradition. There are even a few cases where the editorial hand seems to have added interpretations to existing ideas. But to assume from this that the literature as a whole has not conserved the central ideas propounded by its founder, or even that it was invented ad hoc by redactors, is to lose sight of the distinction between editing and composing. So when we say that the texts were “spoken by the Buddha”, we mean it in this non-literal sense.

My view is probably less optimistic than that stated in the book. I do believe that (some, perhaps most) the Buddha’s actual teachings are contained in the Tipiṭaka, but perhaps not the actual words he used and also potentially his teachings have been enhanced with additional material that he never taught. There may be material taught in other languages that were not translated into Pali and hence not included, I would like to think these have equivalents that were included. More serious are suggestions that some of Buddha’s teachings may have been omitted (or perhaps actively censored) because of the schisms between the various sects that developed in the years following the Buddha’s death. These omissions can be partially compensated by comparing his teachings across the major sects, which have been done by several scholars, notably Anālayo, Sujato, Allon amongst others.

As an alternative view, David Drewes in The Idea Of The Historical Buddha, Journal of the International Association of Buddhist Studies Volume 40 • 2017 • 1–25, argues against regarding the Buddha as a historical figure:

… nothing about him has ever been established as fact, and the standard position in scholarship has long been that he is a figure about whom we know nothing. My only real suggestion is that we make the small shift from speaking of an unknown, contentless Buddha to accepting that we do not have grounds for speaking of a historical Buddha at all. of course, it is possible that there was some single, actual person behind the nebulous “śramaṇa Gautama” of the early texts, but this is very far from necessarily the case, and even if such a person did exist, we have no idea who he was.