I read something online that got me thinking about this. Why didn't Voldemort suspect Snape had defected from the Death Eaters and was now working for Dumbledore during the events of *Philosopher's Stone?
Voldemort was possessing Quirrell's body and his head was protruding from the back of Quirrell's - in other words, Voldemort was with Quirrell constantly during the events of Philosopher's Stone, presumably overhearing whatever Quirrell himself heard.
Snape cornered Quirrell more than once (Halloween, when Quirrell let the troll in, and the night Harry broke into the Restricted Section over the Christmas holidays to look for information on Nicholas Flamel) and openly threatened him against working for Voldemort and pressuring him to declare his loyalties to Dumbledore. This obviously revealed Snape's loyalty to Dumbledore to Quirrell, and presumably Voldemort, and I can't think of a reason why Voldemort wouldn't have been able to hear Snape strong-arming Quirrell perfectly clearly.
Why didn't Voldemort attempt to make contact with Snape during Philosopher's Stone? After all, Snape was supposedly Voldemort's most faithful servant. How is it Voldemort didn't suspect Snape was working for Dumbledore and didn't orchestrate a move against him? Snape wasn't even pretending to be a double agent during Philosopher's Stone, so why Voldemort didn't kill Snape as soon as he was physically able, or have Quirrell attempt to kill him, is unclear.
So yes, why didn't Voldemort suspect Snape as a double agent during the events of Philosopher's Stone?