Hey Brandon,
What you can do is set up your calendar to be the main page of your website. This is done under Settings > Reading > Your home page displays and choose ‘Main Events Page’ as the homepage.
Note however that if you navigate to a different view then ‘events’ will make it back to the slug. There is no built-in option to remove this. You can change it to something different though under Events > Settings > General tab.
When you are looking at specific events then the slug will say something like:
http://domain.com/event/this-is-the-event-slug
‘event’ is also changeable on the same settings page.
Let me know if this helps.
Cheers,
Andras