If an author makes up proper nouns for their text, for example, Bilgebauth, should the very first instance in the text be typeset with an accent: Bilgebáuth to inform the reader of the proper stress for that word, and should the rest of its instances be typeset without an accent mark?
No, accent marks should not be used that way.
In Russian, an accent mark is sometimes used on an unfamiliar word to indicate the position of the stress. For example, the Russian Wikipedia article about Barack Obama spells his name as "Бара́к Оба́ма" the first time, but "Барак Обама" all subsequent times.
However, accent marks are rarely if ever used that way in English, so I don't think that people will understand you if you use them that way.
There is simply no good way to indicate the pronunciation of a word in English; the least-worst options are to give a phonetic respelling (something like bill-geh-BOWTH), or to use a phonetic alphabet such as IPA.