Learn Dutch: De architect heeft nog geen vergunning. - The architect does not have a permit yet.

We use geen because it negates an unspecified noun. In English you say "does not have a permit", which in Dutch translates to having "no permit" (geen vergunning). By putting nog in front of geen, you get nog geen, meaning "no... yet" or "not a... yet". You use nog niet for verbs, adjectives, or specific nouns.

Could I say De architect heeft een vergunning nog niet?

No, that sounds unnatural in Dutch. When negating an indefinite noun like "a permit", you replace een with geen. To add "yet", the adverb nog goes directly before geen, giving you nog geen vergunning.

Does the word vergunning have a recognizable root?

Yes, it comes from the verb gunnen, which means to grant or to award someone something. A vergunning is literally something granted to you, such as a building permit or a license.