Ganz gleich, ob die Anprobe stattfindet, rufen wir an.

Yes, you can think of ganz gleich as a shortened version of Es ist ganz gleich, ob ...

Literally, ganz gleich means something like completely the same or it makes no difference. In this sentence, it works idiomatically like regardless of whether ... or no matter whether ...

So:

Ganz gleich, ob die Anprobe stattfindet, rufen wir an.

is basically the same idea as:

Es ist ganz gleich, ob die Anprobe stattfindet — wir rufen an.

Because ob means whether, not if in the conditional sense.

Here, the sentence is talking about a yes/no possibility:

• Does the fitting take place?
• Or does it not?

That is exactly what ob is used for.

By contrast:

• wenn = if/when
• falls = if, often a bit more tentative

So:

• ob asks about an alternative: whether or not
• wenn/falls set up a condition: if this happens, then ...

This sentence means regardless of whether it happens, so ob is the right word.

Because ob die Anprobe stattfindet is a subordinate clause, and in German subordinate clauses, the finite verb normally goes to the end.

So the word order is:

• ob
• die Anprobe
• stattfindet

This is very normal German subordinate-clause word order.

Compare:

• Main clause: Die Anprobe findet statt.
• Subordinate clause: ..., ob die Anprobe stattfindet.

Because stattfinden is a separable verb.

In a main clause, separable verbs split:

• Die Anprobe findet statt.

In a subordinate clause, they stay together and go to the end:

• ..., ob die Anprobe stattfindet.

So both forms come from the same verb:

• infinitive: stattfinden
• main clause: findet statt
• subordinate clause: stattfindet

Because German main clauses follow the verb-second rule.

The whole opening part

Ganz gleich, ob die Anprobe stattfindet

counts as the first element of the sentence. That means the finite verb of the main clause must come next, in second position:

• rufen = second position
• wir = after the verb

So:

Ganz gleich, ob die Anprobe stattfindet, rufen wir an.

If there were no opening phrase, you would say:

Wir rufen an.

Because anrufen is also a separable verb.

In a main clause, the verb splits:

• Wir rufen an.

In a subordinate clause or infinitive, it stays together:

• ..., weil wir anrufen
• anzurufen

So in your sentence:

• rufen is the finite verb in second position
• an goes to the end of the main clause

It is nominative, because it is the subject of stattfinden.

The fitting is the thing that takes place, so it is the subject:

• die Anprobe = the fitting
• stattfindet = takes place

With feminine nouns, die can be nominative or accusative, so the form alone does not tell you the case. But the role in the sentence does: here it is clearly the subject, so it is nominative.

It is not required, but it can be added.

German often uses ob by itself to mean whether or not, so this sentence is understandable as it stands.

But many speakers would also say:

Ganz gleich, ob die Anprobe stattfindet oder nicht, rufen wir an.

Adding oder nicht makes the contrast more explicit and can sound a little clearer or more emphatic.

Because German very often uses the present tense for future meaning when the context already makes the time clear.

So:

rufen wir an

can mean either:

• we call
• or we will call

depending on context.

In English, future actions often need will, but in German the present tense is very commonly enough.

Ganz gleich is fairly neutral. It works in both spoken and written German.

Some alternatives are:

• egal, ob ... = more informal, conversational
• unabhängig davon, ob ... = more formal
• gleichgültig, ob ... = more formal or written

So this sentence could also be said as:

• Egal, ob die Anprobe stattfindet, wir rufen an.
• Unabhängig davon, ob die Anprobe stattfindet, rufen wir an.

But ganz gleich is a good, natural choice.

German normally uses commas to mark subordinate clauses.

Here, ob die Anprobe stattfindet is a subordinate clause, so it is set off with commas.

The first comma comes after ganz gleich, introducing the ob-clause:

• Ganz gleich, ob ...

The second comma closes that clause before the main clause begins:

• ..., rufen wir an.

So the commas are standard German punctuation here.