Exactly how long after public distribution can a product be copyrighted?

The copyright in a work can be registered at any time -- before or after publication, no matter when. There are significant benefits to registering a copyright: (1) within three months of its first publication date and, (2) before the first infringement and, (3) within the first five years of publication. Registration if done by each of these three dates provides particular benefits. Speak with a California-licensed copyright attorney for more information specific to your circumstances.

It is best to register it within 3 months of the initial publication. However, you can do it before or after then, as well.

As you probably know, once you create a work, you immediately own a "common law" unregistered copyright on that work. Regarding the proper terminology, "copyright" is a noun, not a verb. So what you want to know is the optimal time to register a work for a copyright. As noted, you get many benefits from registering within 3 months of publication, including making sure you can seek statutory, rather than actual, damages in the event of infringement, as well as your own attorney's fees. That make it much easier to find a lawyer if you find yourself needing one. Rather than count days and waiting til the last minute, don't wait, and register as soon as possible after creation.

There is none. Any time! You should register asap!