Uiua, 21 bytes

⍢(+1|¬≍↘¯1≡/+:⊙◫↘,,)1 

Try it!

Starting with n = 1, increment until

• there is no match of
  • dropping the last of
    • the row-wise sums of
      • the n-wise windows of the input
  • and dropping the first n rows of the input

Uiua, 21 16 bytes

⍢+₁(¬≍↘¯1⊃⧈/+↘)1 

Try it!

• ⍢+₁(...)1 Starting with 1, increment until:
  • ¬≍ there is no match between
    • ↘¯1 dropping the last of
      • ⧈/+ the sums of the n-wise windows of the input
    • ↘ and dropping the first n rows of the input