he will have power the dark lord knows not

It was Mrs. Figg who suspected first.
She noticed many things, sitting on her side of her fence with her cats chasing butterflies and nuzzling her ankles, Mundungus and the other watchers dropping by for tea now and then.
Mrs. Figg noticed that Petunia was a nosy bit of work with insecurities hanging from her every harsh angle. She noticed when Dudley learned the word MINE-- the whole neighborhood noticed that one. She noticed that Vernon glared at owls.
She noticed that when Petunia gave Harry a truly horrendous haircut one year, it grew back in at a normal rate. Harry was uneven and weird-looking for ages, hiding under beanies when he could.
When Mrs. Figg had Harry over for carefully miserable afternoons of babysitting, she noticed nothing moved that shouldn't. He didn't accidentally make flowers out of fallen leaves, or levitate anything during tantrums, or turn toys funny colors.
Mrs. Figg called up her mother, interrupting the wizarding bridge game she was winning against the nursing home staff, and asked her how she had known, decades back, that her youngest daughter was a squib.