How did we find out that submarines had been sunk?
Since submarines were frequently operating alone, it would often take a while before their loss was recorded. If the boat was part of a wolfpack, the other members of the pack would likely figure out relatively soon that something was wrong. However, since there was still a chance that the problem was a communications issue, we did not immediately give up hope.
The usual procedure was to identify the submarine as overdue about three weeks after it was scheduled to return to a base. After a couple more months, it would have been declared missing and presumed lost. Families would then have been notified.
We might also get confirmation from the Japanese. Both sides were required to notify the other of the prisoners of war in their custody. However, the Japanese chose not to notify the U. S. of POWs in their worst and most punitive camps. These were the camps where submariners and pilots were initially assigned for interrogation and sometimes for lengthy detention. We might not know about survivors until they were transferred to less punitive camps. That could take a long time. In the worst case, we did not know about most survivors from the USS Perch (SS-176) until the end of the war, 1,297 days after the boat had been sunk in 1942.
A reason that we withheld the information about our losses for some time was so that we were not providing useful information to the enemy. Japan claimed to have sunk more submarines than we ever had. There was no reason to provide the actual information any sooner than we had to.