Learn Polish: Kupiłam sobie mój ulubiony sok. - I bought myself my favorite juice.

Sobie is the dative form of the reflexive pronoun, meaning "to oneself" or "for oneself." Here, it shows who benefits from the action. Saying kupiłam sobie means "I bought for myself," adding a personal touch that you treated yourself to the juice.

How do we know from kupiłam that the speaker is a woman?

In the Polish past tense, verbs show the gender of the speaker. The -am ending in kupiłam tells us a female is speaking. If a man bought the juice, he would say kupiłem.

Why don't the words mój ulubiony sok change their endings, since they are the direct object?

They actually are in the Accusative case because they are the direct object of the verb. However, sok is a masculine inanimate noun (a non-living thing). For these nouns, the Accusative form looks exactly the same as the basic dictionary form.

Can I change the word order and start the sentence with sobie?

It is highly unnatural to start a sentence with sobie. Short pronouns in Polish act like little magnets that stick to the verb, usually right after it. That is why putting it in the second position as Kupiłam sobie sounds perfectly natural.