Thanks for filing this suggestion.

The play button in After Effects, and other playback controls, are in the Preview panel. In the Default and Standard workspaces, you can find the Preview panel docked in the column of panels along the right side (underneath the Info and Audio panels). You can undock and/or reorganize the panels to your liking.

I appreciate that you expect the play controls to be in the same window as the video, which is a common convention for video playback applications. And I agree with you that we should move the playback controls in After Effects. The design After Effects is currently using was made before that convention was common, and had solid logic at its time. While we’ve considered changing that UI, changes to an established application like After Effects come with many complications, and we need to be sure that the benefits of such change outweighs any new problems it would create.

Another way to start a preview in After Effects is by pressing the space bar on the keyboard, which is a common convention in video editing applications. (Note that there are two steps to previewing in After Effects: rendering and playback. The space bar will attempt both, simultaneously, which may be slow if the rendering stage is slow. You can modify the rendering and playback settings for the space bar shortcut, as well as other shortcuts that can start preview and playback, in the Preview panel.)

We’re very interested in what other difficulties you encounter as you learn After Effects. Please feel free to post other requests that you think would make After Effects easier to learn.