Start by creating a batch file with the following contents (replacing the path with your own)
@echo off
echo Starting Counter-Strike: Source...
start "" %1 -game cstrike -steam
echo Waiting for 20 seconds before starting Discord RPC...
timeout /t 20 /nobreak >nul
echo Starting Discord RPC...
start "" /B cmd /c "C:\Path\To\counter-strike-source-discord-rpc.exe"
exit
Next go to Steam and find CS:S, right click it, go to properties and find launch options
Paste the following (replacing the path with your own)
C:\Path\To\batName.bat %command%