I'm exposing my ignorance.....but would anyone be there that early in the morning?
Marine guards would be there 24/7, but probably not many other folks.
No Americans would normally be in the building at 0555 in the morning except the Marine Security Guards who would be in the lobby area. When I was there, the cleaning crews came in around 0630 and were escorted by the MSGs. There were also a few Greek employees who came in to produce summaries of Greek newspapers. US Communications personnel came in around 0700. Whoever attacked the Embassy was apparently not interested in inflicting personnel casualties.
The guards probably, but I would be guessing.