Fun fact: The ancient Egyptian pyramids were built with copper tools, not bronze. Bronze hadn't been invented yet; the Egyptians hadn't established the international trade required to get tin.

They found that copper with arsenic impurities was harder and held its shape better than pure copper, so arsenical copper was cast into basic chisel shape and the edges were cold hammered to work harden them into something that will just about cut limestone for awhile I guess. They also used tube drills and flat saws. They would scatter a slurry of quartz sand and water on the stone to be cut, and then they would work a flat plate of copper back and forth over the sand or rotate a hollow cylinder of copper in place to make a straight cut or drill a hole respectively. In that way they could cut material as hard as granite.

Now as a woodworking tool, even copper is vastly superior to stone in one key way: Ease of repair. You make the bit of an axe out of stone, it's considerably harder than copper, but it's brittle. It's easy to just break, and if you do that you'll never get it back to the same shape because to re-sharpen that bit means napping more of the edge away. A copper axe bit might dull easily, but it can be honed in a minute or so. It bends, rather than breaks.

"Stumbling upon" bronze requires access to tin and knowledge of forging and casting technology. Tin and copper are seldom found near each other, and even if you've got tin it needs to have occurred to you to try melting copper. If you only ever cold work copper, you're not going to figure out bronze.

Hernan Cortes landed on the Yucatan, riding a horse wearing an iron breastplate and carrying a steel sword, and found the Maya and Aztecs living in societies not dissimilar to the Old Kingdom Egyptians. A dude on foot wearing a jaguar skin swinging a wooden club studded with bits of sharp obsidian is scary. A dude on horseback with a matchlock musket and a steel saber is scarier. Imagine a galleon full of 16th century Spaniards dropped anchor at the mouth of the Nile in 2600 BCE and rode into Khufu's Memphis. That's pretty much exactly what went down in what is now Mexico City.