Hybrid Honda Fit 2014

If there's enough power to start the car (ruling out battery/ charging system), no lights on the dash, no codes, and the engine idles strong for the same amount of time (ruling out mechanical issues and key issues) before shutting off, you may have a module malfunctioning or without power. There are several instances of Hondas with a blown MICU (body control/ multiplexer) fuse that idle and then die. CAN bus might also be an issue, but usually that causes all sorts of dash lights.

I would check all fuses, and if everything looks fine use a (dealership level) scan tool that can query different body modules for faults.