Yes.
One factor is how old you are but personally I was easily able to learn enough German in my first eight days in Germany with only a Lonely Planet German Phrasebook to be able to make my own simple sentences as well as manage all the day-to-day situations like shopping, transport, etc.
My German is still terrible - I am hopeless at genders and cases and my vocabulary is tiny - but still ten years later can use the German I learned in a week in Germany to converse with people that have German as a second language.
I am not good enough to converse with native speakers though because even their basic vocabulary is just too full of words I don't know.
Focus on sentence structure. Things like keeping the main verb in second position and other verbs at the end. What can come before the main verb. When you can "invert" the order and put the verb first in questions and additional clauses. The simple version of the past tense where the second-position verb is a form of "haben" and the verb you really want to use is the one at the end in the infinitive.
I found this fun like some kind of logic game. This got me far and I could try to pick up the "rote" stuff by listening and practice. Like vocabulary, which article to use, how to make the plural, pronunciation, etc.
Personally I don't recommend children's books after trying them for language learning. They seem to focus on the wrong kind of repetition and have "colourful" vocabulary such as lots of farm animals. They become boring very quickly for adult readers. This does not apply though if you have a child to read them aloud to!
Much better are adult oriented books that just happen to have very simple sentence forms. Siddhartha by Hermann Hesse is my favourite to try to read in a language I'm learning. My second preference is Der Alchimist by Paulo Coelho.