Immigration rules from the 1950s

[Vonique]

My relatives are from Italy and my mother immigrated to the United States in the 50s when she was a child. She says her mother lied about her age (my mother's age) to get her into the United States. Her parents lied about her age as she was too young and said she was a few years older and thereby was able to gain entry.

She always goes around saying she is younger than what her parents have said she is because of this. She claims that because of all the confusion that her mother really doesn't know how old she is and offers this as proof that she is really younger than how old her family says she is.

My grandmother categorically denies all of this and I've heard her say many times to my mother, "I was there when you were born. I didn't forget the date. THIS is how old you are!"

I've even asked my mother, "Was there really a restriction on how young a child was to be able to go to the United States? That doesn't seem realistic that they would let a 10 year old in and not a 5 year old. And I think it would be kind of hard to make a child look twice her ago."

So my question is: was there really a restriction on how old a child had to be to travel to the USA years ago?

Thanks very much!