Varies by jurisdiction

Until the advent if DNA testing, many US states had statutes of limitations of under 10 years for virtually all crimes except murder.

With the "get tough on crime" and DNA testing, many of those were extended, particularly when there is DNA available, like from where a person touched on a photograph, computer printout, or portable storage media.

However, these aren't retroactive, and in the case of storage media or in some cases on a computer printout, it's not sufficient proof of possession by itself - the fingerprint or DNA could predate the image.

Civil lawsuit statutes of limitations can be retroactively extended, so if you confess to looking at a picture of a particular child, all it takes is an act of your state legislature and your "victim" can sue you for invasion of privacy and more.

Of course, the worse and most immediate damage is to your social network: If you say "I looked at kiddie porn 20 years ago" and you weren't a child or teenager at the time, many of your family and friends will abandon you and your boss may look for ways to get rid of you.