You didn't have 1 year, but you had 1 day old or 2 weeks old, or 3-6 months old, etc.
People never said and still dont' say "this baby is 0 years old". They start at the first complete item of the lower level time units and progress from there...
For ages people use the unit that best captures the spirit of what they want to communicate.
So they may say one hour old, five days old, six months old, etc. a fifty year old typically doesn’t say they are a half centenarian either. Now decades are used to express an age range like so and so is a nonagenarian to avoid being specific.
If you ask kids how old they are, you will often get "5 and a half" etc. They are, correctly, thinking of time as a continuous variable. You "turn 1" when your age reaches 1.0.
