No, you are confused. Of course the universe has many more potential states than a Go board... A Go board is just a 19x19 grid. But the number of possible states of matter in the universe is not relevant. There is still not nearly enough matter to represent every Go state simultaneously in memory, which is what would be required for an exhaustive search of the game tree.

Okay fair enough, it's not as simple as 10^170 > 10^80.

But I don't think your math makes much sense either. You can't just count the number of isotopes - nearly all of the universe is hydrogen and helium. And even with compression, it is going to take a lot more than 1 bit to represent a board state. Memory (at least with todays technology) requires billions of atoms per bit. And that is only memory - the computational substrate is also needed. And obviously we are ignoring some pretty significant engineering challenges of a computer that size, like how to deal with gravitational collapse.

I'll grant that it's potentially possible that you could brute force Go with a Universe-o-tron (if you ignore the practical limitations of physics), but it's definitely not a slam dunk like you're implying.

There are ~10^170 valid board states for Go, and roughly 10^80 atoms in the observable universe. So even with a universe sized computer, you still wouldn't come close to having the compute power for that.

AlphaGo uses neural nets to estimate the utility of board states and a depth limited search to find the best move.