You need to add an entry called extensions.newAddons to your profile settings and set the value to false.
Launch firefox with a custom profile
firefox -profile <path to profile directory>
Type about: config in the address bar and press enter. Right-click on the preferences panel to open the context menu and go to Create → Logical . Enter extensions.newAddons for the preference name. Select false for the new boolean.
The entry should prevent a new add-ons window from appearing when Firefox starts with this profile.
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