While that's great for users who want a clean interface, your document may not be designed with Read Mode in mind - you may have content in a very small <embed> rectangle and want nothing at all other than a vertical scrollbar, or you may have a document where access to the full range of tools is necessary from the get-go. Unfortunately the decision to open in Read Mode is an application general preference (Preferences > Internet > Display in Read Mode by default) and you cannot change that using the initial view settings within a particular PDF file.
The Ninja can leap to the aid of website designers by revealing an undocumented trick.
The "normal" way to embed a PDF file in a web page uses the <embed> tag, as follows:
<embed src="MyFile.pdf" width="530" height="300" />
If you use that, you'll be at the mercy of Read Mode, so the file looks something like this:
If you add the parameter to control the toolbar visibility, Read Mode is disabled no matter what the user's preferences are:
<embed src="MyFile.pdf#toolbar=0" width="530" height="300" />
You can set toolbar=0 to hide it, or toolbar=1 to show it, but either way, the HUD is dead.
If you want to add other preferences, you can - for example this tag turns off the toolbar (and hence the HUD) and also turns off the scrollbar, despite the PDF having more than one page, but turns ON the navigation panes. You can navigate using your arrow keys, or mousewheel:
<embed src="MyFile.pdf#toolbar=0&scrollbar=0&navpanes=1" width="530" height="300" />