Do you know of any English word, however obscure, in which <au> in the spelling has the sound of aʊ as in the proper name Faust?
After a little thought, and consulting Carney’s Survey of English Spelling, I replied as follows.
Lots of people say traumatic with the MOUTH vowel, though others use the THOUGHT vowel. The same applies to various other words of Greek origin (claustrophobia, glaucoma, tau, and trauma itself). You also sometimes get the MOUTH vowel in aural, to keep it distinct from oral. Then there are the actual German borrowings such as meerschaum, sauerkraut, as well as names such as Audi, Schopenhauer, Strauss, like the Faust you mention. There are also geographical names such as Nauru, Palau. And some people use this diphthong, wrongly, in Welsh Blaenau, Dolgellau.
I might also have mentioned other more or less exotic borrowings from various languages, such as luau. And of course there are Latin words: magna cum laude, gaudeamus igitur.
Faust itself has a derived adjective Faustian, as when we say a Faustian bargain. This, of course, is not a German word: the German equivalent is faustisch. So it has to be counted English.
But apart from these, as far as I can see, there are no pukka, echt, authentic native English words with <au> = indubitable aʊ.
I hope my correspondent was satisfied with the answer. Disappointingly, like so many who consult me by email, he didn’t even do me the courtesy of acknowledging my reply.