Hi James and welcome to Electronics Point
The simplest solution would be to short out the Standby button, but the humidifier may require a discrete button-press, and may ignore the button if it's forced ON. But you can easily test it to find out - just hold the button in, then switch on the power to the humidifier, and keep holding the button.
If the humidifier starts up, you've solved your problem - just bridge the two connections on the button. Or preferably, make some reversible modification to keep the button pressed - maybe jam a toothpick down the side of it, if it's recessed, so that it's stuck in the 'in' position.
If the humidifier doesn't start up with the button held in, you will need a circuit that is powered in parallel with the humidifier, that waits for a few seconds, then generates a closure on a relay contact which you would wire across the pushbutton.
This closure may need to be brief (i.e. press then release the button) or the humidifier may accept a continuous closure. Again you can test this by powering up the humidifier, then pressing and holding the button. If it starts up and keeps running, even with the button held in constantly, then you just need a delayed closure. If you have to press the button then release it before the humidifier starts up, you need a delayed brief closure.
Either of those options can be done with a fairly simple circuit, powered from a low-voltage wall wart.
If you can upload a few photos of the inside of the humidifier, we may be able to suggest a simpler solution.
Is it possible that the humidifier has a programmable option to make it turn ON as soon as it receives power?