Nadam se da ću uskoro naći stalni posao u Zagrebu.

Because Croatian often leaves out subject pronouns when they are not needed.

In Nadam se, the verb ending -m already shows that the subject is I. So ja is understood automatically.

• (Ja) nadam se = I hope
• Adding ja is possible, but it usually gives extra emphasis, like I hope.

So the sentence sounds natural without ja.

The dictionary form is nadati se, which means to hope.

This is a reflexive verb, so it regularly appears with se:

• nadam se = I hope
• nadaš se = you hope
• nada se = he/she hopes

In this verb, se is not translated literally as myself/yourself. It is just part of the verb. So you should learn nadati se as a whole unit, not just nadati.

In this sentence, da introduces a subordinate clause: that ...

So:

• Nadam se = I hope
• da ću uskoro naći... = that I will soon find...

Croatian very often uses da after verbs like hope, think, know, say, and similar verbs.

English sometimes keeps that and sometimes drops it:

• I hope that I will find...
• I hope I will find...

In Croatian, da is normally kept here.

Ću is the short form of the auxiliary verb htjeti used to form the future tense.

Here it means will:

• ću naći = I will find

A few future forms are:

• ću = I will
• ćeš = you will
• će = he/she/it will
• ćemo = we will
• ćete = you (plural/formal) will
• će = they will

So da ću naći means that I will find.

Because ću is a clitic: a short unstressed word that usually has to stand near the beginning of its clause.

After da, the normal order is:

• da ću uskoro naći

That is the most natural neutral word order here.

Croatian word order is fairly flexible, but clitics like ću and se have special placement rules, so learners should get used to seeing them early in the clause.

Naći is the perfective verb meaning to find in the sense of reaching a result.

That fits this sentence well, because the speaker hopes for one completed result:

• finding a job

Croatian often distinguishes between:

• naći = perfective, to find, to succeed in finding
• nalaziti = imperfective, to be finding / to find habitually / repeatedly

In this sentence, the completed result is what matters, so naći is the natural choice.

It is in the accusative singular, because it is the direct object of naći.

The speaker is hoping to find a permanent job, so job is what is being found.

Why does it look the same as the nominative?

Because posao is a masculine inanimate noun, and for many masculine inanimate nouns:

• nominative singular = accusative singular

So:

• stalni posao can be nominative
• stalni posao can also be accusative

The form is the same, but the function in the sentence is different.

Because the adjective must agree with the noun in gender, number, and case.

Here:

• posao is masculine singular
• it is in the accusative
• so the adjective also appears in masculine singular accusative

Since masculine inanimate accusative looks like the nominative, you get:

• stalni posao

Also, stalni posao is a very natural way to say a permanent job or steady job.

Because u can take different cases depending on meaning.

Here the meaning is location: the job is in Zagreb, not movement to Zagreb. With location, u takes the locative case.

So:

• u Zagrebu = in Zagreb

Compare:

• Idem u Zagreb. = I am going to Zagreb.
  Here u shows movement toward a place, so it takes the accusative.

This is a very important Croatian pattern:

• u + locative = in, at
• u + accusative = into, to

Uskoro means soon.

In this sentence it modifies naći:

• ću uskoro naći = will soon find

Croatian word order is flexible, so uskoro can sometimes move:

• Nadam se da ću uskoro naći stalni posao u Zagrebu.
• Nadam se da ću naći stalni posao uskoro u Zagrebu. — grammatically possible, but less natural
• Uskoro se nadam da ću naći stalni posao u Zagrebu. — possible with a different emphasis

The original position is the most natural neutral one.

Yes. Very literally, the structure is:

• Nadam se = I hope
• da = that
• ću = I will
• uskoro = soon
• naći = find
• stalni posao = a permanent job
• u Zagrebu = in Zagreb

So the sentence is built very much like:

I hope that I will soon find a permanent job in Zagreb.

That is a very normal Croatian pattern. English often simplifies or drops that, but Croatian usually keeps da in this kind of sentence.