Mielőtt elmegyek, szendvicset készítek a gyereknek.

Mielőtt means before and introduces a subordinate clause.

So:

• Mielőtt elmegyek = before I leave / before I go away

It works much like English before when followed by a full clause:

• Mielőtt elmegyek, ...
• Before I leave, ...

In Hungarian, mielőtt is one word.

Because elmenni and menni are not exactly the same.

• menni = to go
• elmenni = to go away / to leave

The prefix el- often gives the idea of moving away from a place or departing.

So:

• megyek = I go / I’m going
• elmegyek = I leave / I go away

In this sentence, elmegyek fits better because the idea is not just movement in general, but leaving before doing something else.

Because both verbs are in the first person singular form.

• elmegyek = I leave
• készítek = I make / prepare

The endings help show the subject, so Hungarian often does not need the pronoun én (I).

That is why the sentence does not need to say Én elmegyek... or Én készítek... unless the speaker wants extra emphasis.

Because it is the direct object of the verb, so it takes the accusative ending.

• basic form: szendvics = sandwich
• accusative form: szendvicset = sandwich as the thing being made

Hungarian often marks direct objects with -t, but the exact shape can change a little for pronunciation:

• könyv → könyvet
• almá? actually alma → almát
• szendvics → szendvicset

Here, the sandwich is what the speaker is making, so it must be in the accusative.

This is about the Hungarian indefinite vs. definite conjugation.

Hungarian verbs have two main conjugation patterns:

• indefinite conjugation: used when the object is indefinite, non-specific, or absent
• definite conjugation: used when the object is definite/specific

Here we have:

• szendvicset készítek

This uses the indefinite form készítek, because szendvicset here is indefinite: it is a sandwich, not the sandwich.

Compare:

• Szendvicset készítek. = I’m making a sandwich.
• A szendvicset készítem. = I’m making the sandwich.

So the object and the verb form match each other.

The ending -nek is the dative ending. It often means to or for someone.

• gyerek = child
• gyereknek = to the child / for the child

In this sentence, it is best understood as for the child:

• szendvicset készítek a gyereknek = I’m making a sandwich for the child

The article a means the, so a gyereknek is for the child.

Hungarian often allows a bare object noun where English would usually say a or an.

So:

• szendvicset készítek can mean I’m making a sandwich
• egy szendvicset készítek also works, and stresses more clearly that it is one sandwich / an indefinite single sandwich

The version without egy is very natural in Hungarian. It can sound slightly less focused on the number and more focused on the activity itself.

So both are possible, but the sentence as given is perfectly normal.

Because they behave differently in the sentence.

• a gyereknek refers to a specific child, so it uses the definite article a
• szendvicset is an indefinite object here, so it appears without a and without egy

So the sentence combines:

• a definite recipient: the child
• an indefinite thing being made: a sandwich

This kind of mix is very common in Hungarian.

Yes. Hungarian word order is flexible, and changing it changes the focus or emphasis more than the basic meaning.

The given sentence is neutral and natural:

• Mielőtt elmegyek, szendvicset készítek a gyereknek.

You could also say:

• Szendvicset készítek a gyereknek, mielőtt elmegyek.

That still means basically the same thing: I make a sandwich for the child before I leave.

You can also move parts around for emphasis, but not every order sounds equally neutral. The original version is a good standard pattern.

Because Mielőtt elmegyek is a subordinate clause placed before the main clause.

Hungarian punctuation usually separates this kind of clause with a comma:

• Mielőtt elmegyek, szendvicset készítek a gyereknek.

This is similar to English:

• Before I leave, I make a sandwich for the child.

If the subordinate clause comes second, it is still separated by a comma:

• Szendvicset készítek a gyereknek, mielőtt elmegyek.