Absolutely agree with this approach. I’ve been playing for years and having a lot of fun fumbling my way to success. The key is practise until your motor skills will allow you to play anything, a lot of technique is transferable from song to song.

Another suggestion I might add is to try learning to play by ear. This is not for everyone, as musical notation does allow you to get going more quickly, but again with practise you can play most songs near-instantly.

There is absolutely nothing wrong with fumbling around hitting random keys until you’ve got the melody down and adding chords from there. There is also no “right” way to play a song, and lots of people compose their own arrangements, swapping chords or even full note sequences for ones they feel sound better. Playing piano this way is mostly about feeling and using the instrument as a creative outlet.

If you do happen to have access to an electric piano, most of them allow you to record your work, which I also highly recommend doing. Listening to the results during the act of playing the piano is radically different from listening passively. You’ll spot mistakes and form strategies to deal with them in the next iteration.

Last but not least: Try to compile a list of songs you would like to learn, the longer, the better. The worst thing that can happen for your progress is to get burnt out playing the same song over and over again. Either when you encounter something you’re not quite ready for, or when you’re out of ideas. Mixing it up will not only help keep things fresh, but will also allow you to grow and overcome hurdles with other songs that just won’t disappear if you keep trying the same song over and over.

Find your way to play and have fun with it.