How do I make text turn into a button only at a certain time? Is this possible?

This is the effect I would like:

The user is introduced to three things called A, B and C. As they are brought up, they appear on the screen in point for text like this:

  • AAAA
  • BBBB
  • CCCC

Then, after they have been introduced, the user can click on the text to reveal another layer that plays some info. After they've clicked through them all, a button occurs that takes them to the next slide. All of this can be done, no problem, except that I want them to NOT being able to click on the text to show the layers until all of them have been introduced. So let's say for the first 20 seconds I want them to be text, and then after that I want them to function as buttons. 

The way to do this that I have been using is to duplicate the text, turn that into a button, and make this text-button appear in the exact same place as the original text at the 20 mark. The idea being that the user doesn't notice the transition. The issue with this is A.) it's time consuming and B.) it is often impossible to get the text in the exact right spot, such that a slight shift in the placement of the text appears. If it was easier to layer them precisely over top of one another, this wouldn't be a problem.

Any ideas? I'm guessing the solution would employ state changes, but I can't figure  it out. 

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