The Tokyo Marathon is a popular race that runs through tourist areas like Ginza and Asakusa and starts at the government office.
Clearly this を is not the object particle (the race isn't starting the office). I know that を can also mean 'through' like the second time it appears above. But I'm sure the race doesn't start through the office either.
So を must have another meaning I don't know, or it's a typo for で. I assume the former.