Function get_min_lsn 

pub async fn get_min_lsn(
    client: &mut Client,
    capture_instance: &str,
) -> Result<Lsn, SqlServerError>

Returns the minimum log sequence number for the specified capture_instance.

See: https://learn.microsoft.com/en-us/sql/relational-databases/system-functions/sys-fn-cdc-get-min-lsn-transact-sql?view=sql-server-ver16