Some transitions lend themselves to appearing over a background without seeming to need a lead-in (outgoing) clip.
It does need the outgoing clip but we're going to trick it.
I wanted several scaled-down clips to appear over a background and use the Mosaic transition to make the clips appear in tiny Mosaic style.
Simply adding that transition to the beginning of a clip will sometimes affect the whole frame (sometimes not but that's another story). To get around this, highlight the clip and press Option-G to turn that clip into a compound clip. Go inside the compound clip and go ten to fifteen frames in from the beginning and blade the clip into two pieces. Highlight the short clip at the beginning and press V to disable the clip. This short clip becomes the outgoing clip but its invisible. Now apply the Mosaic transition between the clips and stretch the transition to completely cover the outgoing clip. Now step out of the compound clip. The scaled-down compound clip will now make a grand entrance over its background when scaled-down Mosaic squares of the clip turn into the camera and assemble themselves into the clip.