Is this a factory installed Toyota alarm system or an aftermarket installation? Can you post a picture of any security lights or the remote so I can identify the system?
If this is a factory alarm system two things will cancel or override the alarm. Inserting ignition key into the lock cylinder of the door and unlocking the door or inserting ignition key into the ignition lock cylinder cycling the key from off to on three times quickly then go to the start position this should override the system and start the vehicle. These are backup features if the remote does not disarm the system when you hit the unlock button. If these two items do not work the system has to be some type of dealer installed system and not a factory installed system. Without seeing a security light or the remote I can't say for certain.