Has any philosopher proved the existence of an absolute? I'm tempted to say, sure, all of them have. The problem is their absolutes are all dissolute.
Your question is really very broad. You are right that cogito ergo sum is regarded by most these days to contain unwarranted assumptions. The attempt to ground knowledge and reason in some sort of unimpeachable "absolute," whether Aristotelean substance, Thomistic God, or Kantian transcendental subject is regarded these days with grave suspicion. At the very least, we might say it is not exactly the height of fashion.
Perhaps the most fraught and fruitful period of this struggle arose with German idealism, Fichte's "I AM I" and Hegel's "Geist." Today we might say that the "Speed of Light" is a kind of absolute to all possible subjects and measuring instruments in all frames of reference, but I'm not sure anyone knows what that really means.
If you want books on the subject, I'd hardly know where to begin. For a popular overview you might try Jim Holt's "Why Does the World Exist?" It will supply you with many names and viewpoints from philosophy and physics on the question of "ultimate existence," which is at least related to your, again, very broad inquiry.