[kramerica]

Spoiler for theory on my question:

The whole deal with the locked doors may have been all about the students trapped in, and the 3rd years were trying to hack them open. However, the arena itself was not locked.

The other theory is that Cecilia/Houki/etc were already in the arena, just in the broadcast room.

Of course, I'd really appreciate if someone could explain it with or without manga/LN details :P