"It's possible to find music anywhere."

It's not a case of 'natural' - it's simply a question of right and wrong. The verb form following 'It's possible' has to be the infinitive with 'to'. "It's possible to find music anywhere."' -----> correct "It's possible finding music anywhere."' -----> incorrect

It's possible to find music anywhere is really the best and most fluid way to express that. It's possible finding music everywhere is just not something we would say. We may say, It's possible to find music everywhere.

"It's possible to find music anywhere." Correct