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Introduction:

Guide:

%windir%\System32\cmd.exe /c start shell:AppsFolder\Microsoft.MicrosoftEdge_8wekyb3d8bbwe!MicrosoftEdge -private
%USERPROFILE%\AppData\Local\Microsoft\Edge\User Data\Default\Edge Profile.ico

Conclusion:

Sources:

Edge schnell im Privat-Modus starten