You don't. You "technically" don't need gov't-issued identification in public places (with uncontrolled borders, that is) at any time. "Technically." I say "technically" in scare quotes repeatedly because that same technicality is law enforcement's favorite tool in their "I can arrest anyone I want at any time for any reason" toolchest.
If an officer decides to "investigate a potential crime" and further decides you are a potential person of interest to that investigation, he now has the power to detain you (without arrest). Then, since you're now being detained pending an investigation, you can be ordered to identify yourself, including by producing gov't-issued ID. If you fail to do so, they can now claim you are "obstructing," "interfering with" or otherwise "impeding" an active criminal investigation, which is an arrestable offense. It then becomes a separate (arrestable) criminal offense to refuse to identify yourself once you're under arrest.