There is no built in support for this and I don't know of a good way to extend the system to enable this without hacking around to much.
Thank you for a quick answer!
@Linus: I was wondering the same thing, but disappointed to hear it's not in the pipeline.
I think this could be a useful feature for casual editors, as they are probably working more with files than with blocks.
Check this blog post for a potential solution:
Is there a way to change the default tabsettings when opening the resource window in on-page edit mode?