Automate turning on power button for infrared sauna tea sauna?

I have an infrared sauna that turns on with a power button also it has buttons for time and temperature.

As a first step is there a way I can mess with the electrical wires and put some type of rig up to have the power turned on from my phone? I can put a smart plug on the power but I need something to have the power turned on as plugging it in doesn’t turn it on without hitting the power button.