Query entries by matrix date fields for event calendar
I think that in order to do this you are going to need to loop through all events; find eventTimes (within the blocks) that are after the selected date; merge those into an array;  and then return the sorted array. However, by doing so you will loose the ability to easily use pagination. 

Perhaps another solution would be to not use matrix blocks at all and instead create two channels: 1 for 'Shows' and 1 for 'Showtimes' (using your theatre analogy), where 'Showtimes' would be related to 'Shows' using an Entries field-type with limit set to 1. Then finding showtimes would be trivial, and would support pagination, etc. (You could even set the showtimes title to be auto-generated from 'related show title + datetime'.)

And if you wanted to display all the showtimes collected nicely on the Shows entry (for the sake of the client), you can use a nice plugin called 'introvert' to show reverse related entries.