Hello Wajih Arfaoui,
Welcome to the Microsoft Q&A forum.
You don't need to have admin access on the Azure blob(staging layer).
If your linked servie(staging linked service) is using managed identity(which is similar to using your own service principal) authentication then you need to grant "storage blob data contributor" permissions to your synapse/adf workspace managed identity in your staging Azure Blob Storage or Azure Data Lake Storage Gen2 account.
Please follow this document to grant perissions to workspace managed identity.
How staged copy works: https://learn.microsoft.com/en-us/azure/data-factory/copy-activity-performance-features#how-staged-copy-works
Per the document, you need to grant delete permission to your Azure Data Factory in your staging storage, so that the temporary data can be cleaned after the copy activity runs.
"Storage blob data contributor" or "storage blob data owner" roles have delete permissions.
Note:
If your staging Azure Storage is configured with VNet service endpoint, you must use managed identity authentication with "allow trusted Microsoft service" enabled on storage account, refer to Impact of using VNet Service Endpoints with Azure storage.
If your staging Azure Storage is configured with Managed Private Endpoint and has the storage firewall enabled, you must use managed identity authentication and grant Storage Blob Data Reader permissions to the Synapse SQL Server to ensure it can access the staged files during the PolyBase load.
I hope this answers your question. Please let me know if you have any further questions.