Stories are archived 24 hours after publication. When a story is archived, Instagram only shows the number of views—users cannot see who viewed it.
Therefore, you can open the story 5–10 minutes before it is deleted — there is a chance that the user will not have time to see who viewed it. But to do this, you need to know the exact time the story was published. Considering that you can only find out the time by opening the story or following the user’s posts, this is difficult to do.