No, this is not possible, sorry.
Browsers allow Javascript to interact with its core at a certain level, but more on that. The window object provides many functions for interacting with the browser, but the Site Information popup window does not open.
You can read about the Mozilla and Chrome extensions and see how they interact with the browser through JavaScript, but these are only internal extensions, signed scripts, and scripts located on the user's hard drives.
So, if your application needs access to something, the browser should ask the user himself, or you can instruct the user on how to do this.
Hope this helps. :(
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