Para nós chegarmos cedo, precisamos dormir agora.

Because Portuguese can use the personal infinitive, which is an infinitive form that shows who is doing the action.

• chegar = to arrive
• chegarmos = for us to arrive

So:

• para chegar cedo = to arrive early / in order to arrive early
• para nós chegarmos cedo = for us to arrive early

In this sentence, the speaker wants to make it clear that we are the ones arriving early, so nós chegarmos is very natural.

Chegarmos is the personal infinitive of chegar for nós.

Here is the personal infinitive of chegar:

• eu — chegar
• você/ele/ela — chegar
• nós — chegarmos
• vocês/eles/elas — chegarem

This form is very common after prepositions like para, por, sem, antes de, etc., when Portuguese wants to show the subject of the infinitive clearly.

So para nós chegarmos cedo literally works like for us to arrive early.

Because after a preposition like para, Portuguese uses the stressed subject pronoun, not the object pronoun.

• nós = we / us after a preposition
• nos = object pronoun meaning us

Compare:

• para nós = for us
• ele nos viu = he saw us

So in this sentence:

• Para nós chegarmos cedo... = For us to arrive early...

Using nos here would be wrong.

Yes. That is completely natural.

Both are correct:

• Para nós chegarmos cedo, precisamos dormir agora.
• Para chegarmos cedo, precisamos dormir agora.

Including nós adds emphasis or clarity. Omitting it is often more concise and very common when the subject is already understood.

Both are possible, but they use different structures.

• para nós chegarmos cedo → uses the personal infinitive
• para que nós cheguemos cedo → uses para que
  • subjunctive

Both can mean something like so that we arrive early / for us to arrive early.

In many everyday situations, Brazilian Portuguese often prefers the personal infinitive after para when the subject is clear:

• Para chegarmos cedo... sounds very natural.

The para que + subjunctive version can sound a bit more formal, explicit, or structured:

• Para que nós cheguemos cedo, precisamos dormir agora.

No. Here it is best understood as the personal infinitive.

It is true that for many verbs, the nós form of the personal infinitive and the nós form of the future subjunctive look the same:

• personal infinitive: chegarmos
• future subjunctive: quando chegarmos

But in this sentence, the word para strongly points to the personal infinitive structure:

• para nós chegarmos cedo

That is the normal pattern after a preposition.

Because the sentence is talking about a current necessity:

• precisamos dormir agora = we need to sleep now

The present tense in Portuguese often works the same way as in English for this kind of idea.

So the sentence means that right now, in order to achieve the goal of arriving early, we need to sleep now.

In Brazilian Portuguese, precisar can appear with or without de, especially before an infinitive.

So you may hear both:

• Precisamos dormir agora.
• Precisamos de dormir agora.

In Brazil, without de is very common and sounds natural in everyday speech.

With a noun, de is also very common:

• Preciso de ajuda. = I need help.

So in this sentence, precisamos dormir agora is perfectly normal Brazilian Portuguese.

Because cedo is an adverb meaning early, and Portuguese usually places adverbs like this after the verb.

So:

• chegar cedo = to arrive early
• chegarmos cedo = for us to arrive early

This is the most natural word order.

Yes, very naturally in Brazilian Portuguese.

You could say:

• Para a gente chegar cedo, precisamos dormir agora.

This is extremely common in spoken Brazilian Portuguese.

A useful difference:

• nós chegarmos → more formal or more careful
• a gente chegar → very common in conversation

Notice that a gente usually takes 3rd person singular verb agreement in finite verbs:

• A gente precisa dormir agora.

But after para, with the infinitive, you simply get:

• para a gente chegar cedo

Para nós chegarmos cedo is a purpose clause. It explains the goal or purpose behind the main action.

Structure:

• Para nós chegarmos cedo = in order for us to arrive early
• precisamos dormir agora = we need to sleep now

So the whole sentence is built like:

Goal + what is necessary to achieve that goal

This is a very common Portuguese pattern:

• Para passarmos na prova, precisamos estudar.
• Para ela sair cedo, precisa acordar agora.

Yes. It is grammatical and natural.

That said, in everyday Brazilian speech, some people might be slightly more likely to say one of these:

• Para chegarmos cedo, precisamos dormir agora.
• Para a gente chegar cedo, precisamos dormir agora.

The original sentence is still correct and natural, especially if the speaker wants to be explicit about nós.

Yes. Portuguese can easily switch the order:

• Precisamos dormir agora para nós chegarmos cedo.
• Precisamos dormir agora para chegarmos cedo.

These mean the same thing. The difference is mostly about focus and rhythm:

• starting with Para nós chegarmos cedo... emphasizes the goal first
• starting with Precisamos dormir agora... emphasizes the necessity first