Apple has begun introducing support for COVID-19 Exposure Notifications without downloading an app in iOS 13.7, but iPhone users remain in control.
Phase two of the Apple/Google contact tracing plan
Apple is currently beta testing its iOS 13.7 update among developers. The main addition to the new version is the expansion of the COVID-19 Exposure Notification API.
Apple says this will let iPhone users opt-in to receive Exposure Notifications without the need to download an app from your local public health authority.