The goal of most of my steampunk worldbuilding has been to get everyone to meet at the 17th and 18th centuries. Up to that point, my concept of technological development has been very standard and historical; some things get noticed earlier, like movable type or the steam turbine, some social catalysts are moved around to keep cultures from locking into decline, like a small revolution for the Maya or Dara winning in India or Wu being defeated before he can ally with the Manchu or Selim II picking a different war and not losing his fleet. Overall, though, technology develops in mundane ways.
By the 17th and 18th centuries, though, global trade and communication have evolved and all the centers of development are in contact with each other. Most of them are also at war with each other at one point or another. This makes a logical environment to pressurize both technological and cultural development. At this point, we have the perfect explanation for even the wildest extremes of steampunk. Airships, walking wagons (or tanks), automata serving tea, you name it, with all this driving innovation surely there’s some way to come up with it. Perhaps wars between the Mayan city-states are now fought half by ceramic automata, and the fixed defenses are built in the form of big stone statues with movable heads and arms for aiming. Perhaps China has air-based cities, trade cities that travel. Perhaps someone in Europe has collected everything anyone ever wrote about optics and has developed laser guns, vaporization, for the use of.
There is, of course, always the question of the power source. In some cases, spring and steam power are perfectly feasible, though they do suggest that coal and oil extraction also explodes early. In others that doesn’t seem suitable. One point Chron makes is that mineral fuel sources would be unacceptable for some Native American nations, and this suggests the inclusion of magic as a motive force. I like this! And perhaps that development leads some esoteric scholars in other cultures to take a second look at their own traditions. Golems, after all, have a very long history. I can see wind and water power being used for stationary power plants pretty quickly also. If we assume that cities will see the use of power plants early on, then this suggests it might, indeed, be possible for nations to develop particle beams as stationary defensive installations with dedicated plants.
And this gives us the mix which is so characteristic of steampunk: the old with the not-even-here-yet, tall ships with submarines, water clocks with mecha.