Full steampunk, wherein steam power is the apex of human engineering for a long time, is as stated above completely different from having an age of steam while electricity and internal combustion are in their infancy. It would need the invention of basic steam power in an environment where much of the basis for electricity and internal combustion are unknown, an environment where the concept of scientists pushing the boundaries of human knowledge is significantly less prevalent than in post-renaissance Europe.
I've actually pondered on a situation wherein Syracuse defeats Rome sufficiently to bring about a ceasefire due to Archimedes' inventions and possibly some outside help from, for example, Carthage. The Greeks' ally sees the usefulness of some of Archimedes creations better than many of his fellow 'true philosophy should not be sullied by material testing' Greeks and copies some of them. After Archimedes dies, there's sufficient brilliant people around to iterate and improve on his creations, but insufficient driving need not scientific curiosity to invent more efficient pieces of equipment than sets of mirrors and crude steam engines. 200 years after Archimedes dies, the Mediterranean is ruled by wooden paddlewheel-propelled boats that look a lot like triremes, but four or five centuries later the boats are still wooden-hulled if somewhat more hydrodynamic and possibly screw-driven, bronze cannons are seen as the most deadly weapons known to man and there's the general consensus that western society would collapse if the semaphores stopped working.