I was mulling over the question asked by the OP while I was watching some particularly tedious adverts on TV.
I have no memory of anyone ever telling me specifically about god but I do remember at the age of 4 or 5 getting introduced gradually to the idea.
My parents, particularly my mother, were very keen that I went to Sunday School. I hated it and often just went for a bit of a walk instead. I think my parents just wanted a few hours peace on a Sunday morning. Incidentally things were different then and it was no big deal for me and my brother to walk a couple of streets to get to the house where the Sunday school was held. Sunday school consisted of a singing a few hymns, doing a few few prayers and a bit of structured activity like stories and colouring in
When I started school we had a class and school assemblies. It was law then (don't know about now) that schools had to have collective acts of (Christian) worship I believe.
Radio used to broadcast religious services, and on sundays TV had a god spot. Although I didn't listen to them, over the years I was exposed to them in passing.
My point is that exposed to the words to hymns and prayers, and unlucky enough to catch a few words of sermons, attending the odd wedding and christening --- then over a period of time I subconsciously, some might say insidiously, built up a notion of god at at that very early age.
Three years old is too young though. Needs to played down and kept VERY simple at that age.
NB: I became a life long atheist at the age of seven

I just could not seriously take on board all the "fairy stories" the adults were trying to make me believe. Stubborn little monster that I was in those days.