If your database suffers a problem at 3:22 p.m. and your backup was taken at 4:00 a.m., you're probably hoping there is a way to recover the changes made between those two times. What you need is known as Point-in-Time Recovery (PITR).
Regrettably, if you've made a backup with
pg_dump at 4:00 a.m. then you won't be able to recover to any other time. As a result, the term PITR has become synonymous with the physical backup and restore technique in PostgreSQL.
If you have a backup made with
pg_dump, then give up all hope of using that as a starting point for a PITR. It's a frequently asked question, but the answer is still no. The reason it gets asked is exactly why I'm pleading with you to plan your backups ...