The best solution have already been mentioned. I just want to add some thoughts.
The simplest solution is to have a counter and increment on every new file. This works quite well as long as only one thread creates new files. If multiple threads, processes or even systems add new files, things get a bit more complicated. You must coordinate the creation of new ids with locking or any similar synchronisation method. You could also assign id ranges to every proceses to reduce the synchronisation work, or extend the file id by a unique process id.
A better solution might be to use GUIDs in this scenario and do not have to care about synchronisation between processes.
Finally, you can at some random data to every identifier to make them harder to guess if this is a requirement.
Also coommon is storing files in a directory structure where the location of a file depends on its name. File abcdef1234.xyz might be stored as /ab/cd/ef/1234.xyz. This avoids directories with a huge number of files. I am not really aware why this is done - may be file system limitations, performance issues - but it is quite common. I do not know if similar things are common if the files are stored directly in the database.