Ahhoz képest, hogy először égetjük ki a tálat, jól sikerül.

It is a very common Hungarian expression meaning considering that..., for the fact that..., or given that....

So:

• Ahhoz képest, hogy először égetjük ki a tálat, jól sikerül.
• Considering that we are firing the bowl for the first time, it’s turning out well.

Literally, ahhoz képest is something like compared to that, and hogy introduces the clause that explains what that is.

Ahhoz is the allative form of az (that), and it means to that.

This happens because képest normally goes with a noun or pronoun in -hoz/-hez/-höz:

• valamihez képest = compared to something
• ehhez képest = compared to this
• ahhoz képest = compared to that

So even though the whole phrase is best translated idiomatically, the grammar underneath is:

• ahhoz = to that
• képest = in comparison to

Together: ahhoz képest.

Because hogy introduces a full clause.

Compare:

• A tavalyi évhez képest jobb.
  = It is better compared to last year.

But if what follows is not just a noun phrase, but a whole statement, Hungarian usually uses:

• ahhoz képest, hogy + clause

So here:

• ahhoz képest, hogy először égetjük ki a tálat
• considering that we are firing the bowl for the first time

In other words, hogy works a bit like that in English.

Because kiéget is a verb with a verbal prefix (ki-), and in Hungarian the prefix often moves after the verb when another element is in focus.

Basic form:

• kiégetjük a tálat = we fire the bowl

But here először (for the first time) is the focused element, so the prefix moves behind the verb:

• először égetjük ki a tálat

This is a very common pattern in Hungarian.

Compare:

• Megírom a levelet. = I write / will write the letter.
• Ma írom meg a levelet. = I’m writing the letter today.

So the split in égetjük ki is normal and grammatical.

Here először means for the first time.

It can also mean first in a sequence, depending on context, but in this sentence the natural meaning is clearly:

• először égetjük ki a tálat = we are firing the bowl for the first time

So it is not just firstly in a list; it refers to this being the first attempt or first occasion.

Because Hungarian is using the definite conjugation.

The object is:

• a tálat = the bowl

Since the object is definite (a = the), Hungarian uses the definite verb form:

• égetjük = we burn/fire it / we are firing it

If the object were indefinite, Hungarian would use a different form:

• égetünk egy tálat = we are firing a bowl

So:

• égetjük goes with a definite object
• égetünk goes with an indefinite object or no object

Because Hungarian usually leaves out subject pronouns when they are already clear from the verb ending.

In:

• égetjük

the ending already tells you that the subject is we.

So Hungarian normally does not need to say mi (we) unless it wants extra emphasis or contrast.

For example:

• Először égetjük ki a tálat. = We are firing the bowl for the first time.
• Mi égetjük ki a tálat. = We are the ones firing the bowl.
  (This sounds more emphatic.)

Because tál means bowl, and -t is the accusative ending, which marks the direct object.

So:

• tál = bowl
• tálat = bowl (as the direct object)

Since the bowl is what is being fired, it gets the accusative ending.

Also:

• a tálat = the bowl

So the whole phrase means the bowl as the object of the verb.

Jól sikerül means it turns out well, it comes out well, or it is going well.

The verb sikerül often works in a somewhat impersonal way in Hungarian. English usually supplies it, even when Hungarian does not name the subject explicitly.

So here:

• jól sikerül = it’s turning out well / it comes out well

The implied subject is something like:

• the process,
• the attempt,
• the result,
• or the bowl as an outcome.

The important point is that Hungarian does not need to state the subject explicitly here.

Hungarian often uses the present tense in places where English might also use:

• present progressive: we are firing
• or a natural present-time comment: it’s turning out well

So:

• először égetjük ki a tálat = we are firing the bowl for the first time
• jól sikerül = it’s turning out well

This sounds natural in Hungarian. It does not have to mean a timeless general truth; it can describe what is happening now or what is currently unfolding.