No—you cannot flat tow a Mazda 3 under any circumstances. No model year or trim of the Mazda 3 can be flat towed, as doing so can damage the drivetrain, transmission, and front end of the vehicle. Flat towing can also void your warranty and any subsequent insurance claims will likely be denied by your insurer.
However, you still have two other options to tow your Mazda 3. You can use a two-wheel dolly to flat tow the Mazda 3, provided that you lift the front two wheels off the ground. Alternatively, you can use a flatbed trailer to tow either the front-wheel or all-wheel drive versions of the Mazda 3.