The main POD in this timeline is Democrates, who had created a steam engine that used the power of compressed steam to roll a ball around on a pivot point. In OTL the technology was soon neglected and as Marsille declined in importance for the greeks so did this new steam engine. In this timeline though, some Greeks including Democrates brings the technology back to Syracuse and begins to find millitary and economic uses for this strange new device.
Steam Trireme
Democrates discovers that if the steam engine was given enough power to burn, it could actually power a greek trireme. But the speed the trireme moved at was very slow, and Democrates figured that the steam trireme would have to move faster for it to really make a difference in how wars were fought in the world. Democrates was persistent, he hired and worked with many other Greek scientists, and finally devised a trireme that had a max speed that paralleled that of a traditional trireme powered by humans. Although this new technology was very useful, it was confined to Syracuse out of fear that if other countries acquired it, they would turn against Syracuse and destroy them because of their small population.
Macedonia (200 B.C.)(Year 1 After Steam)
After the rise of Macedonia, Syracuse was sort of abandoned as a Greek colony, the Greeks turned their attention towards Macedonia's expansion and ignored Syracuse and their other colonies. Meanwhile, Rome and Carthage were growing and this was starting to concern Syracuse. This prompted a Syracusian invasion of other Greek, and Carthagian colonies. The colonies were terrified by the chugging sounds the steam trireme made, and most gave up without a fight, and the ones who did resist didn't put up much of a fight before surrendering. The same thing happened when Syracuse invaded the Greek mainland, the warring city states were shocked that one of their colonies gained enough power to depose their mother state. Syracuse now controled the entire island of Sicily, and most of Greece. Syracuse gained enough power to rival Macedonia, Rome and Carthage.
Punic wars (56 A.S.)
Carthage and Rome were niceley established empires by now (Rome was still a republic at this time, but we'll call it an empire for simplictiy), and just like baby animals, the young empires hungered for food (territory), they approached each other, and Syracuse and Macedonia, and investigated and sniffed around, then concluded that they were safe to eat, and declared war. The Punic wars were 4 sided, with Macedonia, Rome, Syracuse and Carthage all vying for control of the Mediterranean.