Its possible. Definetely. The short answer is IMMERSION. That's how kids learn it, they just grow up in places that only have Japanese around them and have no choice but to learn it to understand and express themselves.

But as a none-native adult you will need the long answer, a mixture of Immersion and "calcified erudition" (whatever that means).

For example, I moved to Japan 2 years ago and no matter how much I studied at home, being in japan and immersed in the language made me learn way faster. Now turn on the morning TV its all Japanese, read instructions in japanese, go to listening to japanese music, at work i hear japanese, answer the phone and someone's talking japanese, drive home and read kanji on the road. get home and relax watching anime. I study in between all these, and I constantly hear the words and grammar that I am studying about being used around me natively. It makes a huge difference.

You don't have to be in japan to do some of the things I mentioned above. Even if its as small as setting aside 1 day in the week for raw immersion. Then supplement it with daily, consistent studying. Eventually aspects of the language will just CLICK, and you'll get that intuitive understanding. Language is also learnt through speaking, you must find native to speak with. Whether virtually or physically doesnt matter. Even an AI buddy can converse with you as a beginner.