A smink a ruhapróba előtt kész.

Because Hungarian usually omits the verb van = is/are in the present tense, third person when the predicate is a noun or adjective.

So:

• A smink kész. = The makeup is ready.
• literally: The makeup ready.

This is completely normal Hungarian.

But the verb appears in other situations, for example:

• A smink nincs kész. = The makeup is not ready.
• A smink kész volt. = The makeup was ready.
• Kész vagyok. = I am ready.

So in your sentence, the missing is is not really missing — it is just understood.

A / az is the Hungarian definite article, meaning the.

In this sentence:

• A smink = the makeup
• a ruhapróba előtt = before the dress fitting / costume fitting

So both nouns are definite here.

As for a vs az:

• a is used before a consonant sound
• az is used before a vowel sound

Since smink and ruhapróba both begin with consonant sounds, the correct form is a.

Examples:

• a smink
• a ruhapróba
• but az előadás because előadás begins with a vowel sound

Előtt means before here.

Hungarian often uses postpositions instead of prepositions.
That means the word comes after the noun, not before it.

So:

• a ruhapróba előtt
• literally: the dress fitting before
• natural English: before the dress fitting

This is a very common pattern in Hungarian.

More examples:

• a koncert után = after the concert
• a ház mellett = next to the house
• az asztal alatt = under the table

So English uses a preposition; Hungarian often uses a postposition.

Ruhapróba is a compound noun:

• ruha = clothes, dress, outfit
• próba = trial, test, rehearsal, fitting

Together, ruhapróba usually means something like:

• dress fitting
• costume fitting
• trying-on session

The exact translation depends on context.

Hungarian forms compounds very freely, and they are often written as one word, just like here.

So this is not two separate words; it is one compound noun:

• ruhapróba

Here kész means ready, but in English it can often sound natural as done too, depending on context.

With something like makeup, A smink kész can mean:

• The makeup is ready
• The makeup is done
• The makeup is finished

So kész is an adjective meaning something like ready / finished / completed.

A related verb is:

• elkészül = to get finished / to be completed

For example:

• A smink elkészült. = The makeup got finished / The makeup is finished.

Your sentence uses the adjective kész, not the verb.

Hungarian word order is more flexible than English word order, and it often reflects topic and emphasis rather than strict grammatical position.

In:

• A smink a ruhapróba előtt kész.

the sentence first introduces the topic:

• A smink = as for the makeup

then gives the time-related phrase:

• a ruhapróba előtt = before the dress fitting

and finally ends with the key descriptive information:

• kész = ready

So putting kész at the end helps make ready feel like the important point.

A different word order may also be possible in some contexts, but it can change the emphasis slightly. Hungarian often uses word order to highlight what is most important or newest in the sentence.

Normally, no.
That would sound unnatural in standard Hungarian.

With a predicate adjective like kész in the present tense, third person, Hungarian normally leaves out van:

• A smink kész.
• A smink a ruhapróba előtt kész.

Using van here is generally not how this structure is formed.

But remember: van does appear in other kinds of sentences, especially for location or existence, for example:

• A smink az asztalon van. = The makeup is on the table.

So the rule is not never use van, but rather:
with present-tense third-person adjective/noun predicates, it is usually omitted.

Smink is a loanword, and it is very common in modern Hungarian. It means makeup.

Learners often notice that it does not look very traditionally Hungarian, and that is because it was borrowed. Even so, it behaves like a normal Hungarian noun in sentences:

• a smink
• a sminket
• sminkes = made-up / makeup-related, depending on context

So even though its origin is foreign, its grammar in Hungarian is completely regular.