I'm going to propose a new word: prepre. Wikipedia defines 'pre' as, Before; used to form words meaning "in front of (in space)". Before; used to form words meaning "before (in time)". The word prepre uses the word pre in a doubled up fashion to signify, 'what came before the beginning.' Is this decent or am I just awful? DE
I'm going to introduce a new word. Postpre. It means to come after what came before. Am I awesome or awful?
The word you're looking for is "pre-beginning". "Prepre" would signify the penultimate time before now.
Why not prefore? It's a lot easier to pronounce and would probably be easier to figure out the meaning.
Because pre doesn't mean beginning; it means before. On a number line from negative infinity to positive infinity, there are numbers that come before zero. It doesn't make sense to ask what comes before the number that come before zero. The word you're looking for is, simply, pre-beginning.