The Windows app has the option to auto-start the app whenever you log in to your account on the computer. To enable this, simply click Preferences and check Auto-Open at Login. When enabled, Pulse SMS will start itself and open the window automatically. So you'll have access to notifications without having to remember to start the app yourself.
For macOS machines, you can right-click on the dock icon and select the Open at Login option. This is built into macOS.
Linux machines do not currently provide an API for auto-starting the app.