The person who truly believes Tom Robinson has a chance to be set free is Jem. Jem is young, still a bit naive to the ways of society and he believes in his heart that his Father is rightfully defending Tom. Jem idolizes Atticus and he can sense how much this trial means to his Father. Jem can clearly see that Tom did not commit this crime, but he does not understand yet that society will never let a "black man" go free. He is heartbroken when Tom is cconvicted and Atticus is defeated.
In addition, Scout felt the same way that Jem did. Scout later questions one of the lessons learned in school about Adolf Hitler. She actually sees the hypocrisy in how many Maycomb residents are offended at Hitlers treatment of the Jews. Obviously, the townspeople condemn prejudice against Jewish people but show the same type of prejudice towards African American people.
Atticus obviously knew that Tom was not guilty, but did not truly beelive he had a chance to be "set free". Atticus knew the ways of the society in which he was a part. He knew deep down that Tom was likely going to be convicted no matter what he did.