I am reading the relevant parts in
Last Night a DJ Saved My Life now. On Terry Noel they write, ‘Noel mixed records, too. On a primitive set-up – he just had a volume dial for each deck – he would take elements from a track and tease and taunt the crowd with them [...] then he would slam the whole song through the mincer.’ The following text does not explain in detail
why the book’s authors consider him the first DJ to mix records, but from what I gather the DJs before him had silent gaps between the songs they played. They do quote him saying he mixed ‘without losing the beat’, though, but that is a highly ambiguous statement (any two songs can be mixed ‘on the beat’, that does not mean that the DJ is ‘beat-matching’—ha ha, sounding all grumpy here, he is a lovely chap I am sure

).
In a subsequent passage on Francis Grosso, they write, ‘Frank claims he was able to beat-mix – that is to overlap the ending of one record with the beginning of a second so that their drum beats are synchronised – almost as soon as he started. [...] Whether he really did have this ability straight away, Francis was certainly the DJ who made beat-mixing a required skill. He was not the very first to mix [here, I assume, they are thinking of Noel] but he certainly took it to a whole new level, and could hold a blend – two songs playing simultaneously with the beats synchronised – for two minutes or more. [...] “Back then, you couldn’t adjust the speeds,” he [Francis] remembers. “You had to catch it at the right moment. There was no room for error. And you couldn’t play catch up. You couldn’t touch the turntables. I had Thorens at the Haven, and you couldn’t do that on Thorens. All you had to do was start at the right moment.” ’
Since Technics’ SL-1200 turntable, with a rotary pitch control, was released in 1972 it seems likely that someone, somewhere, tinkered with modern-style pitch-changing, but it would be nice to get it from a horse’s mouth.