Bourne walks into the embassy just as the Swiss police show up to arrest him for the incident with the police officers in the park. The embassy lets him in telling the police that they have no jurisdiction there. After they let him in, someone tries to detain him. Jason takes this guy out and then tries to figure out how to get out of the embassy. Dozens of guards with guns start looking for him as he tries to figure out how to escape. He obviously is successful and gets out.
It is amazing the number of movies where someone appears to be trapped in a building with lots of guards, yet they get out: The Fugitive and US Marshals are two movies that use this technique.