I can't think of any easy way to do this in DVDA - the suggestions made by the others might approximate it, but because of DVDA's limitations, it will never look as good as what you see with commercial DVD's.
This is trivial to do with DVD Lab though, or if you're willing to use IfoEdit you could probably edit the DVDA IFO files to accomplish this. In DVDA I'd create 2 menus, with the sub menu being the one with the links that actually take you somplace; that is this is the menu that you want to transition too; render the project to file, then use something like WinDVD to play back and capture a screen shot of the second menu. Then pull the screen shot into Vegas and create whatever transition you want from your starting video to the menu snapshot. Render this out. Then this would become the background video for your first menu. Hide the link on your first menu to your submenu (don't delete it though or DVDA will delete the submenu as well). Render your modified project.
Then using IfoEdit you can modify the end action on the first menu to call the second menu; open the video_ts.ifo, expand vmgm_pgci_ut and select pgc-menu_1, scoll down to where it says "no PCG Command table", right click on the line and select add a Post Command; double click on the command just added and type in the hex 20 04 00 00 00 00 00 02
The only problem with this is anytime you return to the menu, you'll go back to the first Menu/video and then to the menu with the links (which might be ok, depending on what you want).
If you are trying to duplicate the menu intro scene effect this is how I did it.
I rendered all the motion buttons and name tags along with the background and 5 second "intro clip" in Vegas as an MPEG2 file. I entered this as the background on the menu and just used DVDA for the selection overlay. I chose just text and erased all the text so it was a clear overlay then made it an underline. I made it as tranparent as possible then made the color match the color of the background where it would be visible during the intro movie. You can still see it during the few seconds that the "into clip" plays but it is very hard to notice.
So basicaly make it as invisible as possible. Instead of having the overlay fade in you are matching it to the back ground color then making the background fade to a different color.