None of this wouldn't have happened if Sirius didn't decide to go through Lily Evans' things. If the Time-Turner didn't fall out. If Sirius didn't pick it up and start spinning it. But that's what happened.
Sirius was bored. James was flying, Remus was studying, and Peter was sleeping. He decided to try to prank Evans.
Boys couldn't get into the girls dormitory, but being the marauder he is, found a way around it. He started digging through her stuff. While he was throwing stuff out of the way, a little hourglass necklace fell out. Sirius picked it up in curiosity and smirked. He put it in his pocket and ran off back to the boys room.
The boys were back. Remus was reading as usual, James was ruffling his hair again, and Peter was doing homework. Sirius barged in there with the Time-Turner in his hand. Remus panicked.
"Sirius?! What are you doing with that?!"
"Moony, could you calm down? It's probably just one of those Muggle charm necklaces." Sirius said, spinning it in his hands.
"Don't spin it!" Remus warned.
"Moony, chill." James said. Just then, Lily burst into the room.
"Ok I know one of you snooped through my things so-" Lily started. She looked at the spinning Time-Turner.
"Sirius! Did you steal that from my trunk?" She asked.
"Yeah. What's the big deal?"
Suddenly, everything was getting wobbly. Lily pulled Remus and James and put the necklace around them and grabbed Peter. As soon as it had started, it stopped.