Sure with enough language training and practice a non-native speaker can sound like a native speaker.....but that's not easy and is usually the exception to the rule.
I'm assuming from your statements that you have a number of Japanese friends with whom you can speak the language and get a better feel for how to speak like a native speaker. Not everybody gets such luxuries while learning a language.
Except for those who start at a young age (below the critical age, for the linguists here) it's unlikely a non-native speaker will truly sound like a native speaker. Even the best will most likely slip up at least once.
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