Run batch script showing output & recording output to a file

You could run it silently using a Windows Script file instead. The Run Method allows you running a script in invisible mode. Create a .vbs file like this one

Dim WinScriptHost
Set WinScriptHost = CreateObject("WScript.Shell")
WinScriptHost.Run Chr(34) & "C:\Scheduled Jobs\mybat.bat" & Chr(34), 0
Set WinScriptHost = Nothing

and schedule it. The second argument in this example sets the window style. 0 means "hide the window."

Complete syntax of the Run method:

 object.Run(strCommand, [intWindowStyle], [bWaitOnReturn])

Arguments:

• object: WshShell object.
• strCommand: String value indicating the command line you want to run. You must include any parameters you want to pass to the executable file.
• intWindowStyle: Optional. Integer value indicating the appearance of the program's window. Note that not all programs make use of this information.
• bWaitOnReturn: Optional. Boolean value indicating whether the script should wait for the program to finish executing before continuing to the next statement in your script. If set to true, script execution halts until the program finishes, and Run returns any error code returned by the program. If set to false (the default), the Run method returns immediately after starting the program, automatically returning 0 (not to be interpreted as an error code).

Use a computer start up script.

You can do this using either local policy editor (standalone PC or on a domain) or group policy editor (on a domain only.)

Navigate to this settings via

Computer Settings > Windows Settings > Scripts > Startup

The script will run as the local system account