The correct answer to this open question is the following.
What the author means when the text says, "By 1963, she had rocketed from poverty up to the big time, having made ten chart-making hits in only three years," was the following.
The author tried to send the following message with the above-mentioned statement, that by the year 1963, Etta James had reached the pinnacle of his career because she had gone through poverty and being an unknown singer, to sing with famous rock and roll artist and soul singers like Chuck Berry, Little Richard, and Marvin Gayne. At that time Etta has already worked for the famous record company called "Chess Records."