How many of them "drank the Kool aide" so to speak and believed up until the very end they were gong to win? Did any hope that Hitler would've seen the futility of continuing the war and surrender or seek negotiated peace?
It's difficult to say.
Basically in terms of the question we really have two periods of "data." During the war, and after, and both of which have a lot going against them in terms of accuracy.
During the war, there was a lot of incentive to not articulate "defeatist" talk. This isn't to say it'd lead to being shot (although late war, it might just), but it was not a way to endear yourself to your commanders or counterparts and might make your life uncomfortable (or, think in terms of "who do we send to clean the latrines, Hans the proud German Soldat, or Franz the guy who keeps asking why he hasn't seen the Luftwaffe in months and questions how we are still winning if we have only retreated for the last year?"). Additionally diaries were a combination of strongly discouraged or outright illegal (a diary is a great source of intelligence,so keeping one was considered a liability), and letters were read by censors.
So in that getting a good statistical sampling of when the common German soldier knew the war was up from historical documents is difficult simply because there isn't a lot of data points.
Post war of course is influence by:
Being able to look back and know how the war was going to go. I might have thought the Atlantic Wall was going to throw the Anglo-Dogs back into the sea well into late Summer 44....but after the war with access to more information well hell we were likely boned after the 6th of June so that's my "new" answer.
There's a lot of post war German memoirs that were written to simultaneously absolve themselves of blame for the war and separate themselves from the Nazi party. In this, a lot of Germany's enthusiastic military commanders suddenly discovered they had some doubts about the war well after the fact.
Compounding all of this of course would be the simply individual experience and limited information available outside of the soldier's immediate area.
Thus my argument is going to have to be more based upon at what point the writing on the wall would have been fairly obvious. And in that regard I would have to say the failure of the German Winter 44-45 counter-attacks, and the success of the Vistula-Oder Offensive by the Soviets consumed what little reserves the Germans had, and brought the war close/deep enough to Germany proper that it was hard to pretend either front was contained and it really brought home how little there was left to resist the Allies/Soviets.
Of course, some Germans still went to the POW camps well in 1945 swearing that Germany's ultimate triumph was nigh, but by January 1945 there was simply nothing to even give a little cover to the naked lie of German victory.
/u/kieslowskifan gave a reply to "At what point did Germany realize the war was lost? (WWII)" at https://www.reddit.com/r/AskHistorians/comments/2esi1n/at_what_point_did_germany_realize_the_war_was/ck2s3we/
This is a starting point for discussion, not to discourage it. Like with /u/pnzsaurkrautwerfer 's reply, further questions, info, and debate are welcome.