There are asymmetric non-directional tires, e.g, the Michelin Pilot Sport 3 https://www.tirerack.com/tires/tires.jsp?tireMake=Michelin&tireModel=Pilot+Sport+3
Or Bridgestone Potenza S04 Pole Position: https://www.tirerack.com/tires/tires.jsp?tireMake=Bridgestone&tireModel=Potenza+S-04+Pole+Position&sidewall=Blackwall
There are symmetric directional tires, e.g, Bridgestone Potenza RE970AS Pole Position: https://www.tirerack.com/tires/tires.jsp?tireMake=Bridgestone&tireModel=Potenza+RE970AS+Pole+Position
There are also asymmetric directional tires, e.g, Goodyear Eagle Supercar G: https://www.tirerack.com/tires/tires.jsp?tireMake=Goodyear&tireModel=Eagle+F1+Supercar+G%3A+2
As if it’s not confusing enough, there are also asymmetric tires with a somewhat directional tread pattern but which are classified for non-directional use, e.g, Bridgestone Potenza RE-070: https://www.tirerack.com/tires/tires.jsp?tireMake=Bridgestone&tireModel=Potenza+RE070
The bottom line is do whatever is printed on the tire shoulder. If it says “OUTSIDE”, keep that pointed outside. If there’s a directional arrow, mount them so they roll in that direction.
Re the OP Infiniti Q60S, the TireRack.com web site does not list that having staggered sizes, ie different front vs rear. However there are many sub-models and optional packages. Usually an AWD version won’t have staggered sizes, only higher-powered RWD versions.
It’s very important to know what tires your car has, and after a tire service, always check they are mounted correctly. Most factory or experienced independent shops would not mount them incorrectly but it’s always possible.
If you have a high performance car with alloy wheels and there’s a torque spec for the lug bolts, always request the service technician use a torque wrench not an air gun.
If you have problems balancing the tires, have it done at a shop with a Hunter road force machine. To my knowledge, only a road force balancing machine can handle difficult cases.
Some of the advanced Hunter machines have a “match maker” function which can record the “out of round” data from each wheel and tire separately, then match the best tire on the best wheel at the best mounting angle for lowest road force. The technician will typically not do this unless you specifically ask for it, which is normally only done when new tires are installed.
There is a locator on the Hunter.com web site for which shops have road force balancing machines.