Hi @Svatopluk ,
> But how do I (put an attached database to NORECOVERY state) without restoring, please?
No. Unfortunately, it is not possible to attach database with NORECOVERY.
In addition, suggest you using log shipping to prepare this VLDB to primary replica and secondary replica. Select Join Only to start data synchronization as we used Log shipping to keep the VLDB in sync across all servers. Please refer to below blog to get detail information.
Adding a VLDB database to an SQL Server Availability Group
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