Is this for a college application? If so, use that exact phrase. Colleges, at least the ones I'm applying to, want you to shine through the text and be yourself; a formal essay will not get you anywhere.
One of my friends began his essay as, "Once upon a time, there was a kid named Aaron..."
You could say, "As I grew up, I have always...", "Since my childhood...", or "From as far back as I remember...". That last one may be stretching the clause though, I'm not sure. My grammar and word choice is unique due to my Portuguese fluency.