While convenient, infant seats do take up a lot of room. They need to be installed at a 45 degree angle to provide adequate recline for a newborn. Additionally, the Primo Viaggio SIP has a bit of a bulky base, which may contribute to that. However, I don't think it's unusually large.
Are you using handle position A in the vehicle? That will help minimize the space it takes front to back (rather than having the handle down in positions C or D) and I believe it is actually required.
New vehicles aren't necessary. Your son will soon be in a
convertible carseat. Even at a recline for a newborn, most take up less space than infant seats. Once he has good head control, he can be as upright as 30 degrees in a
convertible seat. For now, it may be safest for you to sit next to him in the rear seat rather than cram yourself into the passenger seat.