How to ensure that the users can access the shared files as quickly as possible if the mumbai branch office is inaccessible ?

 preferred service:

Azure file share and Azure file sync 

Use Azure file sync to centralize your organisations file share in Azure files, while keeping the flexibility, performance and compatibility of an on-premises file server.

Azure file sync transforms windows server into a quick cache of your Azure File Share.

You need an Azure file share in the same region that you want to deploy Azure file sync.

Reference:

https://docs.microsoft.com/en-us/azure/storage/files/storage-sync-files-deployment-guide?tabs=azure-portal%2Cproactive-portal