Nunca se me habría ocurrido que pudiera desaparecer una carpeta así de la oficina.

Because the usual pattern is ocurrírsele algo a alguien: for something to occur to someone.

• se is part of this pronominal construction
• me means to me

So se me ocurrió means it occurred to me or I thought of it. In this sentence, what occurred is the whole idea introduced by que.

In Spanish, if a negative word such as nunca, jamás, nadie, or nada comes before the verb, you do not add no.

So these are both possible:

• Nunca se me habría ocurrido...
• No se me habría ocurrido nunca...

They mean basically the same thing, but putting nunca first gives it more emphasis.

Pudiera is the imperfect subjunctive of poder. Here it expresses a possibility seen from that past, hypothetical point of view: that a folder could/might disappear.

• podía would sound more factual or descriptive
• podría would sound more like a straight conditional statement
• pudiera fits the more subjective, surprising, non-factual tone of the sentence

It also matches the past/conditional feel of the main clause.

Because desaparecer is an intransitive verb, so una carpeta is the subject, not a direct object. Spanish often places the subject after the verb, especially with verbs like appear, disappear, arrive, and similar verbs that introduce new information.

So:

• una carpeta = the thing that disappears
• it comes after the verb because that word order is very natural in Spanish

Here así means like that, in that way, or just like that. It adds a sense of surprise, as if the speaker is saying so easily or so suddenly.

In this sentence, it most naturally describes the disappearance, not the folder itself.

Because desaparecer de often means to disappear from a place. The idea is that the folder is no longer there or has gone missing from that location.

• de la oficina = from the office
• en la oficina = in the office / at the office

So de la oficina is the natural choice if the meaning is that the folder vanished from the office.

You will hear that from native speakers, but in standard grammar for an independent clause like this, Nunca se me habría ocurrido is the expected form. Using hubiera instead of habría in this kind of sentence is common in some varieties of Spanish, but it is usually treated as non-standard or more colloquial.

So for a learner, habría ocurrido is the safer choice.