Although I was born here in the states technically I wasn't really properly introduced to English until a few years after I was born. At home, in my early years, my parents spoke nothing but Vietnamese, as they were very zealous about ensuring I would know Vietnamese (oddly enough halfway through my childhood they made a complete turn-around and didn't care, and nowadays they speak more English to me than Vietnamese, which is weird because I'm so used speaking my (broken) Vietnamese to them, so it leads to amusing situations where my dad, say, tells me something in English and I reply in Vietnamese and we go on talking loike that). My lack of English during my early years, despite living in America, is apparent given I had trouble understanding directions from adults when I first went to preschool.
Still, it seems like I quickly picked up English anyways once I stayed at home less and was more or less fluent by the time I left preschool. It helped that 1) I lived in an English-speaking country (obviously); 2) was extremely young, so I could pick up these things very quickly; 3) my parents and grandparents were all fluent in English (and much more fluent than other Vietnamese, even Western-educated ones and intellectuals - their "accent" was practically flawless).
However, it appears I still had a trace of an accent going into high school, and even these days there are still some traces of it, although you'd have to listen really closely - it's most obviously shown through the fact I still can't pronounce the <th> sounds properly after all these years (although I can distinguish them in terms of hearing, obviously) (i.e. I pronounce "three" as "free" and "the" and "duh" (or "ve", sometimes)); among other things, such as pronouncing my vowels somewhat similarly to a stereotypical Mexican. But otherwise at this point I'm pretty much fluent and have been since I was ~5.