Regarding phrase origins, "first use" is often a hard bar to jump. That is true of 'people's champion' and the very similar 'champion of the people'.
The earliest uses of those phrases that I have found were in 1768 (p. 14, about midway through the last paragraph) and 1690 (p. 33, second line), respectively.
'People's champion' appears in George Saville Carey's 1768 Liberty Chastised: or Patriotism in Chains, a farcical play:
...he has once fairly engaged to liberty's and the people's champion....
'Champion of the people' is used in Thomas D'Urfey's 1690 burlesque poem, Collin's Walk Through London and Westminster:
Whilst I the Lump, th'unfinish'd Cripple
Prove more the Champion of the People;