I was wondering if anyone would be able to recommend to me books from a Jewish perspective on the existence of G-d. Something along the lines of proving G-d's existence. I would prefer an evidentiary book, perhaps drawing on Jewish History, archeology, or science. I have already read Rabbi Meir Simcha Sokolovsky's "Prophecy and Providence" (which I would highly recommend), but I was left wanting more examples.
Classic sources: Guide for The Perplexed, Duties of The Heart & The Kuzari.
The contemporary book "Challenge" by Aryeh Carmell seems to be rather popular. A rather different approach is taken by Walter Wurzburger in his "God is Proof Enough"- though I would suggest read the reviews (for example: http://aiwac.wordpress.com/2011/05/03/religion-for-grown-ups-on-r-dr-walter-wurzburger/ ) first, since Rabbi Wurzburger's style is different then the other volumes mentioned here.
"Permission to Believe: Four rational approaches to G-d's existence" and "Permission to Receive: Four rational approaches to the Torahs divine origin" by Lawrence Kelemen. Although not thorough it gives a good introductory insight into some of the arguments that are used in 'proof of G-d' discussions.
chovos halevavos/duties of the heart - shaar yichud / Gate #1 Unity of God
Gate #2 also, but it focuses on reflecting on nature.
I personally have benefited tremendously from the shaar yichud. it's very powerful but only if you really study it in depth.
I haven't read it, but Living Up to the Truth by Rabbi Dr. Dovid Gottlieb seems to fall under what you're looking for and is available for free at http://ohr.edu/992.
An "evidentiary book, perhaps drawing on Jewish History"?!?
"from a Jewish perspective"?
There's this book on my shelf, often read, divided into 3 main subsections, that shows HaShem's influence on Jewish History.....
Good "proof" testimonies at Shemot 19, Devarim 5:3 "not with our fathers but with US, even US, who are all of us alive this day" !!! Powerful stuff.
If you don't accept the validity of the original testimony, from the original witnesses, the commentaries probably won't help much...