Attributive use of the noun 'back-up' (also 'backup') in the sense of "stand-by, reserve" is attested as early as 1952 in OED:
Orig[inally] U.S....Also attrib[utive] spec[ifically] in Computing, (the making of) a duplicate copy of a disc, file, etc., for use in case of loss or corruption of the original.
1952 Wall St. Jrnl. 5 June 18 Value of the stocks, including 'back-up' supplies being held in warehouses for order filling, will total about £1 million.
Use in computing, as noted in OED, is not attested there until 1964; in 1965, the preparation of backup files is implied by the use attested:
1964 CIS Gloss. Automated Typesetting (Composition Information Services) 3 A back-up computer may be located in the same plant or hundreds of miles away.
1965 Proc. AFIPS Conf. 27 193/1 The backup procedures must be prepared for contingencies ranging from a dropped bit on a magnetic tape to a fire.
However, 'back-up' is used attributively in computing, in the phrases "back-up copy" and "back-up file", at least as early as 1957 and 1962, respectively:
When the tape has been written, a copy should be made to serve as a back-up copy. This tape will contain seven binary files.
"TURBO : a two-dimensional few-group depletion code for the IBM-704*, J.B. Callaghan et al., November 1957. Emphasis mine.
Since the punched deck is always maintained up-to-date, it provides a back-up file for the descriptor card catalog.
Electrical and electronic properties of materials information retrieval program, final report, by H. Thayne Johnson et al., June 1962. Emphasis mine.