Honestly, I wouldn't even attempt to grab GL on Immortal. The AI just has too big of a tech advantage on you, and they'll bum rush the GL every time, and even if you do get it, it's too much of a hammer sponge to really pay off in the end. Even though you'll be ahead tech wise, you'll lack the economy to wage a war effectively because you'll have most likely ignored your surrounding resources (unless you were able to snag a worker). By the time you get your infrastructure in line, the AI will be on par with you militarily. It's just not worth it.