Just a quick reminder:

• “un expert”: nominal group (“an expert”)

• “vous êtes un expert”: verbal group (“you are an expert”)

After “Personne ne s’attend à” one doesn’t expect a verbal group: what is expected is a COI (“Complément d’Objet Indirect”) which has to be a substantive. It can be a nominal group:

Personne ne s’attend à sa propre mort.

Or an infinitive group:

Personne ne s’attend à trouver une solution.

Or a verbal group introduced by “ce que”. In that case the verb becomes a subjonctive:

Personne ne s’attend à ce qu’il pleuve.

If you remove “ce que” the sentence doesn’t mean anything else, it just becomes incorrect as you have a non-valid COI.

Ce que is mandatory here. Removing it would lead to a very incorrect sentence:

Personne ne s’attend à vous soyez un expert.

When s’attendre à is directly followed by a verb, that verb must be at the infinitive, e.g.:

Personne ne s’attend à recevoir un expert.

A noun, pronoun or nominal complement can also follow s’attendre à like:

Personne ne s’attend à la venue d’un expert.

Personne ne s’attend à lui.

If you want to append a subordinate clause containing a conjugated verb, that clause needs to be introduced by a conjunction. With direct transitive verbs, that conjunction is commonly que, e.g.:

Personne ne souhaite que vous soyez un expert.

Tous attendent que vous soyez un expert.

With indirect transitive verbs, the prepositions de and à cannot be directly followed by que simply because de que or à que are forbidden combinations in French so a ce is inserted. You can think of this ce as a pronoun for the following clause but it is really part of the compound subordinate conjunction ce que.

Personne ne s’attend à ce que vous soyez un expert.

When the clause is omitted, the pronoun cela (or ça) replaces it:

Personne ne s’attend à cela.

Here are other examples following the same pattern:

Je me suis habitué à ce que vous soyez un expert.

Je ne m’attendais pas à ce que vous soyez un expert.

Je me réjouis de ce que vous soyez un expert.

The previous form is slightly outdated and formal and is usually simplified to:

Je me réjouis que vous soyez un expert.

but this simplification hasn’t occurred yet with s’attendre à so:

Personne ne s’attend que vous soyez un expert.

is incorrect, although it might be heard in very relaxed spoken French.

Note that the following sentence, while looking like the previous ones using de ce que, is a different construction:

Je m’étonne de ce que vous dites.

Here, ce que is what was discussed in the question yours was wrongly suspected to be a duplicate of.