As I had mentioned previously, there is a family of games usually associated with Go throughout China - 方棋 Fangqi - Wikipedia), which is still being played to this day.
Players had been using stones and sticks for each side without problems, and a much smaller board could be easily drawn on the ground with minimum effort (or no board at all, a few imaginary lines are that difficult to picture in the head)
As for archaeological evidence, we already know there were stone beads and what we classified as “stone bubbles” (石泡) or “stone eyes” (石眼) that are pretty uniformed in their sizes, and some with colored pigments left on the surface unearthed that can be dated around the 11th to 16th century BCE. The craftsmanship of stoneworks and bone crafts was more advanced than most people thought, but the era before metal works was dominated by bone tools and stone tools for tens and hundreds of thousands of years. At the same time, they made lots of clay tools and objects also for tens of thousands of years.
Here is one of the oldest “toys” unearthed in China, called 陶響球. And dated about 6000 years to 7500 years ago. And they are hollowed-out stone or clay balls, with incredibly complex designs on the surface, and some extremely thin outer shells. When tied to strings, they can be swung to make particular sounds and played like marble games.
We need to give ancient craftsmen and people a lot more credit for what they can achieve and indeed crafted in their times.