Well the 'start up' screen would be a loading screen (like where the logos show when things load) and I doubt the icon is there.
However, if it is on the screen where say you have to choose what you want to do to get to the main screen (aka swipe to start/lock screen) then you may have some options.
First go into "Settings" and then tap (depending on your Android version) either "Security " and then tap "Enable Widgets" or, in some versions, you will just go from "Settings" to "Lock Screen".
If you have the tap "Enable Widgets" version, you should then be taken to a screen with either the Widgets showing or a plus sign. Here you can add/remove/exchange what shows on the screen, however you cannot change the location on the screen...