Golf a bijection \$\mathbb{N}^n\to\mathbb{N}\$
APL (Dyalog Unicode), 13 10 bytes

(⊢+1⊥∘⍳+)/

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Similar to other answers, since the Cantor pairing is bijective, compositing \$n-1\$ Cantor pairings is bijective as well.
(       )/  ⍝ reduce the input with following function
       +    ⍝ left argument + right argument
      ⍳     ⍝ the first left+right positive integers
   1⊥       ⍝ convert those from base 1 (sum)
 ⊢+         ⍝ + right argument