The prequel doesn't have to feature Yamato. Kind of like the Babyon 5 prequel movie about the Earth-Mibari War didn't feature Babylon 5 at all. But had several of its characters in it.
They have the Interplanetary Wars between Earth and Mars that lead into Earth's attitude when Gamilas arrive and the whole eight years of the Space War until 2199. Okita is prominent during that time.
The ships used at the Battle at Pluto were old. Almost 30 years old. And these were what was left of the UN fleets after eight years of war with the Gamilas. All that is left is the Far Eastern Region's force of 21 ships (it looks like 30 launched from Earth on that last campaign, but only 21 made it to Pluto, and only 1 made it back to Earth). The Space Battleship Kirishima was one of eight ships in its class built starting in 2171. So there were more ships, and one has to assume the Americans and Europeans had better ships early in the war. Just that after eight years...well all you got left is the old Japanese ships.
Until they launch the newly built Yamato. (it is no longer the original ship sunk in 1945).