Where can one access Aland's 23rd edition which was used for the first edition of the New American Standard Bible (NASB)? Where can one access Aland's Novum Testamentum Graece, 23rd edition, which was used for the first edition of the New American Standard Bible (NASB), according to this PDF?
The 23rd edition of Nestle-Aland was published in 1957, and unfortunately, Google Books often does not have preview available for books of this age. This edition is no exception, at least right now. It thus appears that used book stores are going to be your only option.  

Depending on your country, the most appropriate online book shop may vary.  Abe Books is a good bet in the US at least.  A search for 1957 editions currently reveals one potential match.