There are several ways to accomplish this. To set a few registers or bits you can place Set Bit or Set Word objects on the common window (window #4). These objects have an option for Set On when window opens:
Because the common window is always visible objects placed on this screen will be triggered once when the project starts.
Another option is to use a macro. The SetData function can be used to write directly to PLC registers:
And the macro editor includes an option to Execute one time when HMI starts: