1. You cannot prove God exists. Philosophy has well established this and all the arguments to the contrary are meant for those who do not understand why the arguments all fail.
2. Anyone trying to show from Archaeology that there is evidence for the biblical accounts is generally limiting themselves to interpretations of the material given by a handful of “biblical archaeologists.” The majority of the time the claims made by these are based on ignoring the problematic evidence or are based on too little evidence. To understand what I am saying, go to Aish.com and find articles on Archaeology and then go do a web search for that same item and see if when all the evidence is added up it makes sense to conclude the way that Aish presents it. I have found it does not.
3. The OP asked for help in approaching Yom Kippur from a standpoint of struggling with belief. He specifically asked not to get into proofs for and against religion as there are plenty of other threads here and in other places that have debated this issue a lot. If you want to be helpful, give him so inspiration to help get through Yom Kippur.