Hello and welcome! I’m very honoured that this is your first post
I think your post copied and pasted itself halfway through that happens to me sometimes - I have no idea why. Anyway.
You’ve made a pretty good go of it, to be honest - it’s not the friendliest first sentence.
Are you familiar with relative clauses? They occur all the time in Japanese, and are basically clauses that modify / describe a noun. The equivalent in English would be things like:
A book that I read yesterday
A man who lives on my street
A house which is blue
In Japanese, the descriptive clause instead goes before the noun, and is written in plain form. The descriptive clause itself can be fairly complex, and it can end with an adjective or a verb.
This is all a very long-winded way of saying that that phrase you’re asking about is a relative clause. ある日 is a common expression meaning “one day”. It’s actually a very mini relative clause all of its own, which you could understand literally as “a day that exists”.
So ある日 is effectively a noun itself.
Then we have しばらくたった, which you’ve identified correctly. Together I’d interpret it as something like “some time has passed”. It’s important not to dissociate it from the beginning of the sentence:
So it’s time that has passed since (から) the incident of the vanished goldfish.
Altogether, we’re describing “a certain day” which occurs some time after the incident of the vanished goldfish:
In nice English:
“One day a little while after the Case of the Vanished Goldfish…”
that was so long, sorry - does that help?