How long does it take for collectibles to be worth something?

If you are talking about online collectibles then they don't have any value of their own. They gain value if they become popular or people start buying them.

In other words, if collectibles become a form of entertainment then they gain value. That for example, crypto kitties weren't really valuable at the start but they gained value after many people started playing the game.

People were playing the game because it was fun. The value of the virtual kitties came from the fact that people were paying attention to them and were having fun playing that game.

So, if you are buying online collectibles then their worth depend on whether they will become popular or not in the near future. Personally I do not like this idea. Because the risk is too high.