KIEV, Ukraine—At first glance, the glass-walled offices of Golos look like a tech start-up. Young volunteers in jeans and hoodies are ensconced in orange bean bags, frantically tapping away at their laptops. It's 6 o'clock in the evening, but no one looks to be going home any time soon.

These offices, in central Kiev, are the epicenter of political change in Ukraine, where voters elected a comedian with no political experience to be president, and appear hungry for a fresh batch of lawmakers to lead them through a critical juncture in their country's post-Soviet history. To some, it's a do-or-die moment for Ukraine's push to become an advanced democracy.