Κοιμάμαι μόλις βάζω το κεφάλι μου στο μαξιλάρι.

Here μόλις means as soon as.

That is one of its very common meanings when it introduces a clause:

• Μόλις έρθει, θα φύγουμε. = As soon as he comes, we’ll leave.
• Μόλις βάζω το κεφάλι μου στο μαξιλάρι... = As soon as I put my head on the pillow...

Be careful: μόλις can also mean just in other contexts:

• Μόλις έφτασα. = I just arrived.

So the exact meaning depends on the sentence.

Because the sentence describes a habitual / repeated situation, not one single event.

Greek often uses the present tense for things that happen regularly:

• Κοιμάμαι μόλις βάζω... = I fall asleep / I go to sleep as soon as I put...
• In natural English, we also do something similar: I fall asleep as soon as I put my head on the pillow.

So this is not really about right now. It means this is what usually happens to me.

Because κοιμάμαι is one of those Greek verbs that has middle/passive-style endings but an active meaning.

So although -μαι often looks passive to learners, it is not always passive in meaning.

• κοιμάμαι = I sleep / I am sleeping / I go to sleep
• It does not mean I am slept

English learners often think -μαι = passive, but that is too simple. In Modern Greek, some verbs simply use this set of endings as their normal form.

In this sentence, it most naturally means I fall asleep or I go to sleep.

That is because of the context:

• as soon as I put my head on the pillow

This clearly suggests the moment of drifting off, not just the general state of being asleep.

If a speaker wanted to be extra explicit, they might also say:

• αποκοιμιέμαι = I fall asleep

So:

• Κοιμάμαι μόλις βάζω το κεφάλι μου στο μαξιλάρι is natural
• but Αποκοιμιέμαι... can sound even more precise

Because βάζω is the present/imperfective form, and here it matches the habitual meaning of the sentence.

The idea is:

• Whenever I put my head on the pillow, I fall asleep

If you were talking about one future occasion, Greek would usually prefer:

• Μόλις βάλω το κεφάλι μου στο μαξιλάρι, θα κοιμηθώ.
• As soon as I put my head on the pillow, I’ll fall asleep.

So the contrast is roughly:

• βάζω = repeated / habitual
• βάλω = one completed future act

Because Greek usually doesn’t need subject pronouns when the verb ending already shows the person.

• κοιμάμαι already means I sleep / I am sleeping
• βάζω already means I put

So εγώ is normally omitted unless you want emphasis or contrast:

• Εγώ κοιμάμαι μόλις βάζω το κεφάλι μου στο μαξιλάρι, αλλά ο αδερφός μου όχι.
• I fall asleep as soon as I put my head on the pillow, but my brother doesn’t.

This omission is very normal in Greek.

Because the normal Greek order for this kind of possessive is:

• article + noun + possessive clitic

So:

• το κεφάλι μου = my head
• το σπίτι μου = my house
• η φίλη μου = my friend

For an English speaker, it may feel backward because English puts my before the noun. Greek usually puts μου, σου, του, etc. after the noun.

So μου το κεφάλι is not the normal standard way to say it here.

Because Greek normally uses the definite article together with the possessive clitic:

• το κεφάλι μου = my head
• το χέρι μου = my hand
• τα μάτια μου = my eyes

This is especially common with body parts, family relationships, and many everyday nouns.

So to an English speaker, Greek may look like it is saying:

• the head my

But that is simply the normal Greek structure.

Στο is the contraction of:

• σε + το = στο

So:

• στο μαξιλάρι = on/to the pillow

In Modern Greek, σε is a very common preposition, and it combines with the definite article:

• σε + το = στο
• σε + τη(ν) = στη(ν)
• σε + τα = στα

This is something you will see constantly in Greek.

Because after σε, Modern Greek normally uses the accusative.

So:

• το μαξιλάρι is the accusative form here
• στο μαξιλάρι = on/to the pillow

In Modern Greek, case usage after prepositions is much simpler than in Ancient Greek. For learners, the important rule is usually:

• σε + accusative

Yes, Greek word order is fairly flexible.

The sentence as given:

• Κοιμάμαι μόλις βάζω το κεφάλι μου στο μαξιλάρι.

is a natural, neutral way to say it.

But you could also say:

• Μόλις βάζω το κεφάλι μου στο μαξιλάρι, κοιμάμαι.

That version puts more focus on the as soon as... part first.

So the original order is not the only possible one, but it is completely normal.

It sounds like a general truth / habit.

It means something like:

• This is what usually happens to me
• I’m the kind of person who falls asleep immediately

If you wanted to describe a single event in the past or future, Greek would normally change the verb forms:

• future: Μόλις βάλω..., θα κοιμηθώ.
• past: Κοιμήθηκα μόλις έβαλα...

So the present tense here strongly suggests a repeated pattern.

Yes, it is natural and easy to understand.

It literally means I put my head on the pillow, which matches the English idea well.

A speaker might also use other verbs in similar contexts, depending on style:

• ακουμπάω το κεφάλι μου στο μαξιλάρι = I rest/lean my head on the pillow
• ξαπλώνω = I lie down

But the sentence you have is perfectly normal Greek.

Yes. A very common slightly more explicit version would be:

• Αποκοιμιέμαι μόλις βάλω το κεφάλι μου στο μαξιλάρι.

That makes the fall asleep idea clearer.

Still, the original sentence is absolutely fine and natural in everyday speech. It simply uses:

• κοιμάμαι in a context where the meaning is clearly I fall asleep quickly.

So the original is good Greek; it is just not the only way to express the idea.