R’ Shimshon Pincus ZTZ”L had this very discussion with R’ Ezriel Tauber SHLIT”A. He said that he would first be Makriv a Korban before Giyur. R’ Tauber responded, “That’s because you have always known you were a Jew and therefore take it for granted. When I was a child in Europe, to save me from the Nazis, I was raised by Goyim and I didn’t even find out I was a Jew until I was 9 (or 10?). Being Jewish is so precious to me that I wouldn’t delay for even one moment!”