How long does it take to enroll in the Developer Program (Organisation)
Apple makes an API call to D&B to look up DUNS numbers, so it's basically instantaneous. It's pretty clear from the wording of the response that Apple isn't the hang up here.
- When DUNS is already set - registration takes me a day or so typically to enter everything in Apple - see that the API call matches - clear up any issues with zip code or business name between how I entered the company name in D&B and how it's entered in Apple (a space before a comma can break the API lookup - it's very precise in my experience and fails if you don't have every character exactly matching in the two systems).
Assuming you haven't made a clerical error that's causing the DUNS lookup to fail, You'll want your business manager or corporate legal department to contact D&B and expedite the listing. D&B does accept money to expedite their listing process so you could always pay your way to an official "credential" from them if it's taking too long to go down the "I'm a small business and want you to verify my credentials for free when you get to it" path.
If you are a solo developer, you might find it easier to just make a personal account and sell your apps without needing D&B if you won't use that listing for other reasons. This really is a business decision about how your LLC or incorporation is set up and not really an Apple question other than this is one of several hoops they require businesses to jump through before they enter a legally binding agreement with your business.
I would add, that joining as an enterprise takes far longer, weeks to a month if you have your legal council ready, records match and add month or two if there are hiccups like someone already signed up your company or an account is frozen or locked.
Check if your organisation has a D-U-N-S number. The developer program enrollment shouldn't take a month. If you have the D-U-N-S number handy, share it with Apple and it will expedite the enrollment.
You can refer to these links from Apple Developer Support:
D-U-N-S Number
Enrollment
It is recommended you contact Apple Developer Support for further help.