**EDIT: they will often let you try out a class, for free. You have to visit the schools and talk to the instructors. See what they ages are, for signing up etc.
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Karate.
Jiu Jitsu, commonly starts kids at older ages.
Karate, younger.
My Daughter takes Karate and loves it very much. She is 8 and started when she was about 7.
At her Dojo, they start kids at 5 years old.
Due to developmental ability per attention span and ability to follow directions, and physical motor-skills coordination, and being potty-trained- per the age.
Each school, has set ages, they start kids at.
So you have to consider that.
A real Dojo/school, will not start kids real young. It is also their physiological development. As our Sensei said, in real young children, their joints/ligaments etc. are more flexible and not developed yet, so in hyper-flexed moves, they will not feel 'pain' as an adult would. Feeling pain is also a keen head's-up, per safety etc.
Also, some Dojos might have "Toddler" classes... but this is not 'real' traditional martial arts, training/teaching. It is modified, per it being Toddlers. Or they give away belt colors/levels, very easily... not it being based on REAL skill and ability or understanding.