In recording terms, 'track' originally referred to the groove:
Originally Posted by mercia
'a. = groove n. 2c (now rare or Obs.)':
1904 S. R. Bottone Talking Machines & Records 60 We must have some means of controlling or varying the pressure of the stylus of the reproducer on the record, so as to enable it to follow correctly every indentation in the ‘track’.
But the earliest example, according to the OED, of the word meaning an individual item, or section ('hence, a single recorded item (esp. of popular music), which on a long-playing record is a band bounded on both sides by an area of widely-spaced grooves), comes from The Gramophone (no further details as to the recording being referred to),':
1956 Gramophone Dec. 265/1 None of the tracks lives up to the promise of the star-studded personnel.