You can export an APK build from Unity that allows the game to be installed to an Android device without the need for Google Play Store during development, this is what we use for quick tests. You would be able to share this with people by uploading it somewhere and providing a link, but people would have to be willing to set their device to 'Allow Unsigned Apps' in order for it to run. Unity's own instructions for building are here: https://docs.unity3d.com/Manual/android-BuildProcess.html
Hope this helps, and good luck with your game!