Yes, enter it it the File Info dialog; File > File Info or Ctrl/Cmd + Shift + I
Is there a way to View that at first glance in PDF without going through Additional Info tab..
No. The Document Properties dialog must be called up. I have one idea, but since you were trying to save a step, this may not be ideal...
When you open a PDF, (in Acrobat, of course), 3 things can be visible:
1. The document (page + bleed + slug; as you've already explored)
2. Acrobat's panels; Pages, Bookmarks, Navigation, Attachments
So, if there is non-page information you want shown when an Acrobat user opens your PDF, you could add that info to a Comment or "Sticky Note." I haven't tested it exhaustively or anything, but when I add a sticky note, then right-click and choose Open All Popups, then Save...the open popups persist and are visible when I reopen. This would serve your purpose and also stay out of the print workflow.