Howdy xanati,
Sadly there is no easy way to do this. You would likely be interested in this feature request though. Definitely throw a few votes its way if this is something you want.
Now, it is possible, but it is a pretty in depth customization and thus requires a fair bit of PHP and WP API knowledge. The function tribe_get_events(), which is documented a bit more here (most of which is still relevant to 3.x), allows you to easily pull event content anywhere. You can even wrap that up in a shortcode if you are familiar with the WP shortcode API. But, the issue is that all of the JS, CSS, and resources that are normally loaded up on an events page will not be queued yet. You will need to huntdown which files need to be enqueued for your particular call, then enqueue them. A bit of a pain aye?
If you simply want to the event calendar your home page, a lot of sites, even on our own demo done, simply runs an .htaccess redirect from example.com/ to example.com/events/.
Does that all make sense? I certainly hope so. Let me know if I can clarify anything or be of further assistance. Cheers!
– Brook