The timing of this topic is almost unreal. I just made a topic: Grammar Predicament - #11 by greasyButter
I started with Japanese the way you want to. I wasn’t very serious in the beginning though. I started to watch anime and listen to music. Now, the thing is this method will take a long time, to really get that intuitive understanding.
You should go through this link one of the user’s posted on my topic: How I Struggled with and Overcame Japanese Grammar - Japanese Level Up