Precisamos de apoio técnico para resolver o problema.

Precisamos is the 1st person plural form of precisar, so the subject is we. Portuguese does not need to say nós here, because the verb ending -amos already shows who is meant.

You could say Nós precisamos..., but that usually adds emphasis or contrast.

Because precisar normally goes with de when you say what is needed:

• precisar de ajuda
• precisar de tempo
• precisar de apoio técnico

So precisamos de apoio técnico is the standard pattern: to need technical support.

In Portuguese, adjectives often come after the noun. So apoio técnico is the normal order.

That is different from English, where we usually put the adjective first: technical support.

Usually yes. Apoio técnico is a natural way to say technical support or technical assistance.

A useful nuance:

• apoio técnico = broad technical help/support
• assistência técnica = can also mean technical support, but often suggests repair service or after-sales service

So in this sentence, apoio técnico is a very good choice.

Because the sentence is talking about technical support in a general, indefinite way, not a specific support service already identified.

So:

• Precisamos de apoio técnico = we need technical support / some technical support
• Precisamos do apoio técnico da empresa X = we need the technical support from company X

The article appears when the support is specific.

Para resolver shows purpose. It means to solve or in order to solve.

So the structure is:

• Precisamos de apoio técnico = main idea
• para resolver o problema = why we need it / for what purpose

It is very common to use para + infinitive like this in Portuguese.

Because problema is a masculine noun, even though it ends in -a.

This is common with several words of Greek origin ending in -ma, for example:

• o problema
• o sistema
• o tema
• o programa

So the correct article is o, not a.

O problema means it is a specific problem, probably one already known in the conversation or situation.

Compare:

• resolver o problema = solve the problem
• resolver um problema = solve a problem

Portuguese often uses the definite article when the speaker has a particular thing in mind.

Yes. A very natural alternative is:

Para resolver o problema, precisamos de apoio técnico.

This puts more focus on the goal first. The original version is also completely natural and neutral.

A careful European Portuguese pronunciation is roughly:

[pɾɨsiˈzɐmuʒ dɨ ɐˈpoju ˈtɛkniku ˈpaɾɐ ʁɨzuɫˈveɾ u pɾuˈblɛmɐ]

A few useful pronunciation notes:

• the final -s in precisamos sounds like zh before de
• unstressed vowels are often reduced in European Portuguese
• the r at the start of resolver is the stronger Portuguese r
• para is often pronounced in a reduced way in everyday speech

So in fast speech, it may sound more compressed than the spelling suggests.