Also, you don't need to "toss [your] documents", I'm not sure why you think that's required to initiate an asylum process lol
Someone versed in EU law can chime in, but I imagine that being literally undocumented would only make the process harder (though it would be abundantly clear that you're an American anyways)
Indeed, they will need to check your story, and that's a whole lot easier when they know your identity (otherwise they have to verify your identity in other ways, which will certainly take more time...).
Also, you don't need to "toss [your] documents", I'm not sure why you think that's required to initiate an asylum process lol
Someone versed in EU law can chime in, but I imagine that being literally undocumented would only make the process harder (though it would be abundantly clear that you're an American anyways)