Is there a type of database that can directly recall an element given a pointer in O(1) time?
Most RDBMS (with transaction support) are general purpose and picks a tradeoff between reads, writes, deletes operations and storage (memory/disk) requirements. Your requirement is very specific to your use-case. I don't think you will find any database optimized for it.

Basically you are looking for some kind of array lookup. Otherwise it will not be O(1). Do you really have only a put and a get operation. No deletes ?