I have a vague memory that Steffi Graff made it to No. 3 before her first win.
You are certainly in the right region. Steffi was ranked at 6 at the end of 1985, and won her first title in April 1986 - but I have no idea what ranking she was at the time.
I was one out; she was #3 seed but #4 ranked. I found the final of her first win on Youtube: https://www.youtube.com/watch?v=2XrRazCCPOQ
YES YES YES YES YES! Get in there Jo you absolute beauty. Superb to be able to regroup and come back strong after such a tough period at the end of the 2nd, and again at the end of set 3 saving break points with a fantastically constructed point and a couple of aces. Finally over the line on the 3rd MP and that's 470 points and $128k. Not too shabby. So happy for Jo :)