Is there a way to fetch vault id just by a given wallet address?
Yes. Fireblocks now provides a reverse-lookup endpoint for this:
GET /v1/vault/lookup_by_address?address=<BLOCKCHAIN_ADDRESS>
The response includes the owning vaultAccountId and the blockchains associated with the address.
Java:
fireblocks.vaults().lookupVaultByAddress(address);
The endpoint is currently marked as beta. A 403 means the feature is not enabled for the workspace, while a 404 means no owning vault account was found.