How do I create a time search option in WordPress?

I am developing an event search website in wordpress and I would like to know if I can build a time search option.

Here is what I mean:

My site will do 2 things:
(1) Let event organizers enter information about events, including a start time and end time for the event by using a form on the site (which will be hooked up to a MySQL database in the background)
(2) Let users search for events by name and start time, e.g. search for “Patty’s lunch” at “2 pm”

In point (2), letting users search for an event by name is easily done. But how do I create a time search so that users can search for an event start time like 2pm?

Is there a plugin for this? If not, does anyone know a workaround?

Please help!!! If I can’t do this, I may have to abandon WordPress altogether!!!

Thanks!