My oldest started playing T-ball at around 5-6, daughter played soccer at 8, my two youngest son's started soccer at about 6-7.
Daughter started soccer at 7 and played through college. One son played football starting at 5 but we saw how many injuries the other kids sufferred and the coaches kept telling them to shake it off. Not my kid.
They have to show interest first. I started both when they were young. Around 4-6 years of age. Back then it was cute little hoards of little tikes are flocking to where the soccer ball was on the field and me and the wife dressed in fall warmth with a hot coffee in hand.
If your child isn't interested in sports its more of a chore then anything else. It's best to start little things like kicking the ball around the house or playing catch in the back yard.
My youngest son wanted to play T-ball when he was 5. He ended up playing baseball through his senior year in high school. My daughter was in track and field from 9th grade (15 years old) through her senior year running hurdles and throwing javelin.
I believe my son was about 4 when he took soccer through the Y. Other sports followed as his interests grew.
My son was never interested in sports so he never played them.