When did the ISBN numbers for books start?

The ISBN system began officially in 1970 when it was adopted by the ISO.

The International Standard Book Number (ISBN) is a unique, numerical[1] commercial book identifier, based upon the 9-digit Standard Book Numbering (SBN) code created in the UK by the booksellers and stationers W.H. Smith and others in 1966.[2] The 10-digit International Standard Book Number (ISBN) format was developed by the International Organization for Standardization and published as an international standard, ISO 2108, in 1970.

https://www.newworldencyclopedia.org/entry/International_Standard_Book_Number

It was first created in 1965 by Gordon Foster, Emeritus Professor of Statistics at Trinity College, Dublin. Then improved by David Whitaker and Romanian Emery Koltay.

The Standard Book Numbering (SBN) code is a 9-digit commercial book identifier system created by Gordon Foster, Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers WHSmith and others in 1965. The ISBN configuration of recognition was generated in 1967 by David Whitaker (regarded as the "Father of the ISBN") and Emery Koltay (who later became director of the U.S. ISBN agency, Bowker).

https://en.wikipedia.org/wiki/ISBN

Some interesting history of the ISBN system here:

Since 2007, the ISBN in the U.S. has featured 13 numerals. You can separate the numerals into different parts. Reading left to right, the first four numerals represent the prefix element; the next two, the registration group; the next four, the publisher; the next three, the title; and the last, the check digit.

https://bookscouter.com/tips/whats-an-isbn/

In 1965, W. H. Smith (the largest single book retailer in Great Britain) announced its plans to move to a computerized warehouse in 1967 and wanted a standard numbering system for books it carried. Their consultants devised the Standard Book Numbering (SBN) system in 1966 and it was implemented in 1967.
The International Organization for Standardization (ISO) Technical Committee on Documentation (TC 46) set up a working party to investigate the possibility of adapting the British SBN for international use. As a result, the International Standard Book Number (ISBN) was approved as an ISO standard in 1970, and became ISO 2108.

http://www.isbn.org/standards/home/isbn/international/history.asp