Ofcourse there is always a way, one way or the other, which works!
If you're just trying to look around, and see the various directories and files in your deployment, you can enter the site's "Kudu" dashboard, using the url format http://<yoursitename>.scm.azurewebsites.net
This will give you a web-based dashboard, including a debug console (web-based) where you can explore your various directories (and the directories will show up visually as well).
More info can be found in this post from the Azure Websites team.
Hope it helped!
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