Launch Android application without main Activity and start Service on launching application

You said you didn't want to use a translucent Activity, but that seems to be the best way to do this:

1. In your Manifest, set the Activity theme to Theme.Translucent.NoTitleBar.
2. Don't bother with a layout for your Activity, and don't call setContentView().
3. In your Activity's onCreate(), start your Service with startService().
4. Exit the Activity with finish() once you've started the Service.

In other words, your Activity doesn't have to be visible; it can simply make sure your Service is running and then exit, which sounds like what you want.

I would highly recommend showing at least a Toast notification indicating to the user that you are launching the Service, or that it is already running. It is very bad user experience to have a launcher icon that appears to do nothing when you press it.

Yes you can do that by just creating a BroadcastReceiver that calls your Service when your Application boots. Here is a complete answer given by me.
Android - Start service on boot

If you don't want any icon/launcher for you Application you can do that also, just don't create any Activity with

<intent-filter>
    <action android:name="android.intent.action.MAIN" />
    <category android:name="android.intent.category.LAUNCHER" />
</intent-filter>

Just declare your Service as declared normally.

The reason to make an App with no activity or service could be making a Homescreen Widget app that doesn't need to be started.
Once you start a project don't create any activities. After you created the project just hit run. Android studio will say No default activity found.

Click Edit Configuration (From the Run menu) and in the Launch option part set the Launch value to Nothing. Then click ok and run the App.

(Since there is no launcher activity, No app will be show in the Apps menu.).