Had a similar experience at a dining hall in college:

- Walk into crowded dining hall

- See a big round 8 seater table with only a backpack at one seat

- Only available seat so I place my tray with food down in the opposite seat

- Pretty girl ends up sitting at that first seat. Kind of cool (especially since this is an engineering campus)

- her 6 other friends sit down at the table

- I didn't know what to do so silently and VERY awkwardly finished my meal as they were all joking around and having a great time

- Got up and left once I was done

- I should add: at no point did anyone ask me who I was or make any comments towards me

Today me would totally have either excused myself and joked about it or made small talk with the "I am totally a the wrong table" as an opener