Zombies, Run! 5K Training is a separate app from the main Zombies, Run! app, and does not contain a base building feature. You can only build a base in the standard Zombies, Run! app.
It’s also not possible to pick up Supplies or Materials in the 5k Training app and have these count towards your base in the main Zombies, Run! app.
The 5k Training app was intended to be a more structured series of workouts to help people gain running experience, rather than the free form running used in the main Zombies, Run! app. We wanted to make sure that each app could be used separately from each other, so it’s for this reason the 5k Training app does not have this feature.