I'm a non native speaker who has reached native-level fluency in English, and I have never looked at a conjugation table in my life. The only experience I have is thousands of hours of reading/listening, and maybe a couple hundred hours of speaking.
BTW I think most native speakers would write 'non-native' instead of 'non native'.
Learning is an effort that needs to be put. Preferably, in a time frame narrow enough you don't forget why you even started learning. And when optimizing the language learning process, grammar tables are useful.