If you know C++ programming already, you could try Unreal Engine. It's quite the beast of game engines, and by having so many features, it's a tall wall to climb to actually understand all of it, but there's nothing you can't do with that engine. And the art path and support for high-end art features is second to none.

If you want an easier start, and you don't really have art to take advantage of all the fancy features in Unreal, you could try a simpler engine like Godot. You'll probably be learning their custom scripting language for that, but you could also open/build from the base engine in C++.

Most games use some kind of engine, either publicly available, or developed in-house, because you need, at a minimum, some kind of game editor to build the “levels” in, and building the game and the editor on the same fundamental technology is quite helpful to see what you'll get in game, and when doing that, something in the shape of an “engine” will pop out.

However, if your art is simple, and if you prep it all in Maya/Blender, Photoshop, and text files, you can get away with building just “a game” with no particular “engine” on the inside. For a single-person scoped game, that's probably the easiest way to get started, if you choose to roll your own instead of using a pre-existing engine. Building your own engine alone, especially when you don't have experience to draw on, is a common way to never build a finished game …

Depends on your current proficiency with programming, but if I know C# and C++ well enough, I would probably choose Unity or Unreal, which are scripted using those languages.

Since your game involves vehicular gameplay, it helps that Unreal has two templates (Vehicle and Vehicle Advanced) that you can use as a launchpad. Unity has a guided tutorial about a karting game, which can be a good resource to follow. To learn things truly, don't forget to tweak things and play around with stuff to make the game your own.