Push off! - Push Button

Hello, I have a hard drive media enclosure. When power is connected it requires you to push a button and release it an instant later to turn it on(if you hold the button in too long it resets the settings) I want it to turn on immediately without a button once the power is connected. How can I bypass the mechanical switch nuisance? I guess I need something that'll be a closed circuit for a second and then immediately become an open circuit across the existing switch connection...It's got me stumped tho! Any whizz's know how this could be done?