The easiest option is to start a minimized thing. Label purpose:
cmd /c START /MIN \path\to\test.bat
or
cmd /c START /MIN cmd /k ( ping 1.1.1.1 -w 10000 -n 1 && @ECHO All OK)
It is not hidden or something else, but it does not appear on the desktop or, worse, steals focus.
If you want the window to go away by itself, "cmd / c ..." will do this. "cmd / k ..." will leave the window open.
Plan B is mentioned by @CodyGray in a published SU link. There are programs that do not open windows, such as wperl, pythonw, or wscript (initially available on Windows). If you can transfer your command to one of these things, then you can effectively double-click the icon and run it silently.
If Perl were available, I would, of course, agree to this, because you can create fairly powerful single-line files that do not require the creation of other files.
wperl -MWin32 -MNet::Ping -e "$p=Net::Ping->new('icmp',10000); if ($p->ping('192.168.1.1')) { Win32::MsgBox('Ping Successful', 1 + MB_OK, 'All Good'); }"
In your example, you combine the teams together, the last one is the notification. If you do not want the window to be open for the first command, it would be inconvenient to do this for the second when you notify the user of something. After invoking the "cmd / c start cmd / c @echo Everything OK" process, this would probably do, but using the CMD windows to notify the user was probably not the kind that the HCI guys would welcome.