You can't get rid of it -- but, if you click on the Settings box in the upper right corner, you can set it to automatically open the program when it launches. Then you can manually close it.
Meantime, Ozpeter has created a utility for sidestepping the Welcome Screen. It may be the solution you're looking for.
With PrE8 & 9 there are two ways to launch PrE, and one has a bit more of a "welcome screen." The normal shortcut, placed on the desktop upon installation, goes to the longer "welcome screen," but there is another executable, that only gets the "Splash Screen." Not sure if that is possible with PrE 7 though. Others, with PrE 7 can probably give you that verification, and should be able to point you to the exact executable file for the more "streamlined" Splash Screen, if one exists.
For general Splash Screens, there is really no by-pass, and the Splash Screen can be very useful, in that it tells you what version/update you have (in most cases), and also shows what is being loaded. If the launch does not work, one can often see exactly what the faulting module was - usually the last to appear on the Splash Screen.
Good luck, and wait a bit, to let a PrE 7 user comment,
Thanks everyone for the quick replies. I guess I'll just move on with it there. I am building Packages to deploy out to the user's in our organization. Our accepted way is to generally get rid of all splash screens. But as long as I know there is nothing I can do I should be able to deflect the complaints that land at my desk.