I was born and raised in a non-English speaking country from the ages of 1-5 before moving to America to start kindergarten (in American English.) So while I didn't start learning English right after birth, I was still exposed to the language early on. It is also the language I think in and know the best. Would I be considered a native speaker of the English language?
The most widely accepted definition of "first language" is the languages acquired within the the so-called critical period - a period in which children are highly sensible for the development of linguistic competences - in which one's mother tongue is usually acquired, or conversely, everything which is learned after one's first langauge is fully acquired is called a second language.
Since that critical period spans at least up to the fifth, some even say up to the 13th year of one's life, and you probably still were within your critical period (or your very first language was not fully complete yet) when you started to learn English, probably one could say that English is indeed a native language for you.