Now you could put a heading at the opening of the story. Something Like August 1812 and that would let the reader know when they were. You could also say something like Fresent Day. Ten years ago. These would tell the reader but they're stale ways to show what you want the reader to know.
Using show and tell is a help. Have the characters in a conversation speaking of something that belongs to the period. Miss Mary Brown turned to her cousin. "When we go to Brighton, will we see the Regent." This would give the reader a real clue to the when on the story.
The July sun shone relentlessly on the mountain climbers. This will also tell a bit more about the when.
Try something like. The incessant ring of the alarm caused Susan to groan. Six thirty is too early to be up but there were things to do and places to be.
All these ways show how to give the reader clues as to when the action is happening. They will keep them reading.