Review the item:
Since he had fallen asleep on the library sofa,
William was unaware that his twenty-eight algebra classmates were
sweating, sighing, and wracking their brains as they tried to ace their
final exam, poor William, on the other hand, was quietly earning a zero.
The comma between sofa and William is completely correct. Since he had fallen asleep on the library sofa is a subordinate clause, so it cannot stand alone. William was unaware is a main clause.
When a subordinate clause introduces a main clause, you need a comma between them.