JavaScript (Node.js), 62 6060 58 bytes
f=(n,i=0i=n,s='')=>i<n=>i?[...Array(n)].map((_,j)=>f(n,i+1i-1,s+j)):s
Try it online! OutputTry it online! Output is 0-indexed. Edit: Saved 2 bytes thanks to @JoKing and a further 2 bytes thanks to @Arnauld.