Doing the same computation, but this time with upper limits for computing systems. There is a theoretical limit for the number of computations a universe sized computer can do: roughly 2.8 × 10^229 operations.
Let’s assume the number of computations per move is at least equal to the square of the board size S (although a quantum computer may be more efficient than that?). The number of moves in a game is roughly S squared.
So a theoretical limit of S for a computer the size of the universe would be the fourth root of 2.8 × 10^229 operations = 3.0 x 10^57.
This AI would not be able to finish a game on a 10^58x10^58 board in its lifetime of 10^132 years.
Edit: fixed calculation error