There's an Upcoming Events indludelet added by default to the homepage of new sites, in the Right column. Includelets don't do anything if there's nothing to show, which is why it didn't appear before you created some events in your calendar.

So you can remove this, or move it to a more suitable place, as you see fit!

There are various options for the includelet, like how many events to show, and whether to show image/description, but I'm not sure if there's an option for showing the time.

Please do have an experiment with it and report back! :-)

Thanks

Joe