For Switzerland, you need to know the "Heimatort" (place of origin), because it remained the same place even if they moved to another town. All the birth, marriage and death records were and are also registered at the Heimatort. Since 1875, the civil registry offices are in charge, and before 1875 the churches officially registered b / m / d. Some municipalities started early with family registers (in Canton Bern also called "Bürgerrödel" - "Bürger" means citizen).
So your next step would be to get the page of Daniel Eduard Allenbach and Anna Grossenbacher in the Heimatort Adelboden. The family registers are often sorted by marriage date of the couple ("before 1881" for the couple above), and the registers have an index. So it shouldn't be that difficult to find their page. The family registers always have references to the pages of the sons and of the parents of the husband, which makes research very easy.
Difficulties: you would need a permit to get copies for the years 1875-1929. Before 1875, no permit is needed. Of course the permit is quite expensive and copies cost a fee too. I don't know it they would send you a scan - I only got paper copies a few years ago, and I also had to tell them the exact volume and page numer to get copies.
Next difficulty is that the family registers are of course not kept at one single archive, but at the regional civil registry office. Adelboden and Hasle bei Rüegsau are not in the same, but at least the permit is for the whole Canton of Berne.
Depending on the Heimatort, some family registers only started in mid 19th century, while some were written backdated to mid 18th century.
So you might need a professional genealogist for this task. But as you already have quite some information, it hopefully wouldn't be too expenisive to hire one.
Then, when you get back further than family registers exist, you will need the church records. Also here it depends on the Heimatort / municipality, but often they started in late 16th century or 17th century. Here, you should always find the birth / marriage / death at the location of happening, but also at the Heimatort. Sometimes you will need to look at the "Auswärtige" or "Augsburger" books, where those not living in the Heimatort were recorded seperately.
Nearly all church books of Canton of Berne are published online at the Staatsarchiv Bern.
I hope this helps.
Ps: what a great birth record! Thank you for sharing!
