You just need to start it with startService() somewhere. This will prevent it from being stopped automatically when there are no more bindings.
From the Service documentation, emphasis mine:
A service can be both started and have connections bound to it. In
such a case, the system will keep the service running as long as
either it is started or there are one or more connections to it with
the Context.BIND_AUTO_CREATE flag.
As others have pointed out, it could still be killed by Android if resources are needed. You can “prioritize” your Service and make it less likely to be killed if you make it a foreground service.