If you'd like this to be your life's project, and you have a lot of free time... maybe.
But why making a game without an engine? I tell you to get an open-source game engine.
By doing this, you are not as dependent on the engine itself and its flaws and weaknesses.
If you want something the engine doesn't have, you simply change it, add the feature you need, compile the engine and use it.
Don't like how the functions work? Build an interface or even rewrite them!
If your changes are really for the better, they could even be peer reviewed and added to the engine itself!
Building an engine would really be a waste of your precious time, adding years of development to your project, so you can have a similar or even worse result.
As you're telling me you'll be using your free time and expect no return from the project other than the amusement of seeing it come to life, but still don't want to waste money on and get stuck with an engine, I see no other option than this: get an open-source engine.
Increase your own chances of actually finishing the project someday.