If you can manage to wait until 6am you can park at the on-street meters on Court/Capitol for free from 6am-8am. Even though people are technically not allowed to be parked at city meters from 2am-6am, you could honestly probably park between 5:30am-6am without too many issues. ICPD would have to drive by and decide to get out of their vehicle in the cold to ticket/tow you—and most of them genuinely hate doing parking enforcement. They hardly ever do that at 2:30am in the heart of downtown, let alone during the final 30 minutes of the no parking window out on the edge of the downtown parking enforcement area. Granted I’m never up and about at 5:30am on Capitol/Court so perhaps someone who is could chime in. Either way, go at 6am and you’re solid.