This quotation very likely doesn't stem from Heisenberg. Of course, this is very difficult to prove. But there are two major aspects that lead me (and others) to believe that this is in fact correct:

a) This quotation is always presented without a source - or the source given is simply another book, which either gives the quotation without a source, or cites another book that....and on and on and on. To make it short: Not a single source is citing an original source, e.g. a publication by Heisenberg, or a letter. Not even a letter by a different person with something along the lines of "Heisenberg once said...". The quotation seems to have appeared out of the blue.

b) The quotation is assumed to be a translation from German. Surprisingly, there are multiple German versions ("Der erste Trunk aus dem Becher der Naturwissenschaft macht atheistisch, aber auf dem Grund des Bechers wartet Gott"/ "Der erste Schluck aus dem Becher der Wissenschaft führt zum Atheismus, aber auf dem Grund des Bechers wartet Gott." /"Die Naturwissenschaft ist ein Kelch bei dem der erste Schluck atheistisch macht, aber am Grund wartet Gott"). This also leads to the assumption, that the quotation was (made up or not) originally in English.

Please keep in mind, that none of this actually proves that the quotation is a later forgery. It just makes it very, very likely.