Typically, the 429 error occurs when you have too many deployments/failed deployments of an App Service Plan within a short period of time. This causes the system to throttle any additional deployments for the next 48 hours.
I understand that you have already mentioned you cannot wait for another 48 hrs. Based on your requirement/scenario, you may provision in other regions or subscriptions.
You may create an Azure support request for a focused assistance on this specific issue.
Checkout references to similar discussion thread/doc:
- App Service Plan Create operation is throttled
- App Service Plan Create operation is throttled for subscription
- Understand how Azure Resource Manager throttles requests
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