This seems like a great task as a test for AI.
The result is easily verify-able, yet the techniques to design such a glider are very complex and some might not have been discovered yet.
You can change "might not" to "have not".
The Game of Life is Turing complete. And therefore a complete analysis of how to write programs in it would imply a solution to the Halting problem. Which is impossible.
It's already being done. Has been done for decades now. Definitely wouldn't be a good use of an LLM-type model if that's what you're proposing
If you look at the placement of Journal of Cellular Automata in SciMago's Shape of Science visualization[0] you'll see that it's completely surrounded by machine learning/AI journals
[0] https://www.scimagojr.com/shapeofscience/