Q.   Where is the best place to open a splash screen on program start up?

A.   The best place to open a splash screen is in the project source  file after the first FormCreate and before the Run  This is  accomplished by creating a form on the fly and then displaying it before the app is actual opened.

 program Project1;

uses Forms,  Unit1 in 'UNIT1.PAS' {Form1}, Splash;

{$R *.RES}
var
  SplashScreen : TSplashScreen;  {in the Splash unit}
begin
try
SplashScreen := TSplashScreen.Create(Application);
  SplashScreen.Show;
  SplashScreen.update; {To paint the splash screen}
  Application.CreateForm(TForm1, Form1);
  {
   do other CreatForms or any other processing
   before the app is to be opened
  }
 SplashScreen.Close;
finally  {Make sure the splash screen gets released}
  SplashScreen.Free;
end;
Application.Run;

end.