It always seems impossible until it's done.
The real story
Quote Investigator found no evidence this statement appears in any book or speech by Nelson Mandela. The Nelson Mandela Foundation's quotes database returns no results for this phrase. The earliest attribution to Mandela located by Quote Investigator appeared in an Australian newspaper in 2001. The general sentiment has a far longer history: Pliny the Elder (died AD 79) wrote "How many things, too, are looked upon as quite impossible, until they have been actually effected?" Similar expressions also appear in works by Robert H. Goddard (1921) and Robert Heinlein (1951). The Mandela attribution appears to be a modern, unverified accretion. Africa Check has also confirmed no record of Mandela saying this.