Pulling date data with jQuery

a future version of the plugin is likely to have some data attributes in the calendar template elements with timestamps and you could have your script to read them

you can have a look here but it’s currently a beta not safe to use in your live sites: https://github.com/moonstonemedia/WP-Google-Calendar-Events/tree/refactor

but I can’t assure about their portability… at some point would like to output calendar data using the json REST API – that would be more reliable to use