SQL Server find database without backup from a given date

Here I am giving you sample query to get database list which are not having backup since date.

SELECT          S.NAME AS database_name,  
    'Nobackups' AS [Backup Age (Hours)]  
FROM master.dbo.sysdatabases S 
LEFT JOIN msdb.dbo.backupset B    ON S.name  = B.database_name  and b.backup_start_date >'20201101'
WHERE B.database_name IS NULL AND S.name <> 'tempdb'
ORDER BY  B.database_name

Other Refrence

SQL Server database backup history

Restore database in SQL Server TSQL Statement

Backup History using TSQL