According to this PS3F story, SCEJ is now allowing Japanese PS3 owners to download a LittleBigPlanet theme and get the chance to be entered into the game's beta. From the piece:
According to the details given, applications to the beta will be accepted from September 17th to September 23rd. The beta itself will take place from September 29th to October 12th. The size of the file will be 950MB. In each region (Japan, Europe and North America), 20,000 users will be selected for a total of 60,000 users. Hopefully we'll hear about how North America and Europe can get in on the act soon.
More through the link. No confirmation on when this is going to happen in Europe as yet.