no. itch is just a place to post already existing things. There's no development environment built into itch. An engine is a program that handles a lot of the nuts-and-bolts required to create a game  (like, for example, displaying images to the screen, handling basic physics calculations, that sort of thing), and often organizes things in a way that logically make sense when creating games. So unless you feel like writing your own engine during a game jam (would not recommend), you'll probably need an engine. But you don't need to go for one of those beefy heavy-duty ones like Unity or Unreal if you don't want to (or don't have the disk space lol)

Scratch (here) is probably the most well-known starter programming environment. No typing code required, you just drag and drop logic elements, and there is lots of documentation and tutorials on how to use it. It's got an in-browser version these days, so you don't have to download any software. 

Construct (here) is more powerful but also has drag-and-drop logic so no knowledge of programming necessary. Also has a browser version :) 

Another reply mentioned pico-8, which is also a browser engine with a basic logic handler that's pretty easy to pick up.

There are plenty more, but these are a good place to start looking