Should I aim to create my own game engine as soon as possible?

Having a game engine gives you a quality boost in the features that you implement into your game. So say your game engine has 3D graphics V1 and you use that in your game, your graphics are going to produce more design points (and possibly tech depending on the stat, I'm not sure), resulting in a higher quality game overall. These will increase your ratings and sales.

It's like software projects in the real world. If you have a framework to work with from the start, you don't have to spend as much time on the back end and you can focus on the fine details.

Game Engine Parts: There are some features that you need to have in an engine to use in your games.

I would recommend creating a game engine as soon as you can. There really isn't a reason not to if you are producing profitable games. It doesn't take a lot of time for a simple 2D linear story engine, and you'll see the rewards immediately.