But anbox is already running a flavor of AOSP, which is android without google (unless you meant android without google code, in which case you will have exactly nothing to run). AOSP can entirely be built from source, everything is Apache2-licenced, and it does not contain or require the gapps. Now you can add most gapps APIs (in order to make apps that rely on them work) through the microg project, or you can install the official google services using opengapps.