Are you sure your car has the factory alarm system? Look at the button bank & see if one of the buttons on the right side has an icon of a tow truck towing a car. If you have that button, your car has an alarm. If you car doesn't have an alarm, your fob will still have a red panic button that should sound the horn when depressed. I believe those cars equipped with the factory alarm also activates the horn when the panic button is depressed. The horn for the alarm is separate and much higher pitched.
Bob is correct.
If your smart has the factory alarm you will hear a “chirp chirp” from it when you hit the lock button and a single one when unlocking.
The button on the dash he’s referring to is for the microwave and tilt sensors for if someone does get into the car or wants to steal it by pushing it((tilt sensor)
The panic button(red button) on the key is for the panic alarm which uses the horn even if you have the factory alarm(tried it soon after I got mine)
YouTube has a few videos that let you hear what the alarm sounds like when it’s triggered(though it’s much louder in person)