It's more than just one sentence in EE1.
You need to remember the context in which Xande began his empire. After the Second Umbral Era, magic was taboo. Xande collected the descendants of priests and witches from the Second Astral Era and formed a powerful mage corps. None of his enemies had magic or at least anything close to the extent that he did. It's like bringing bombs to a battlefield where everyone else is hitting each other with sticks. In that context, it's very easy to create a powerbase and the conquer everyone else around you and form an empire in 1 year, exactly as the book describes.
The Allagans also had Ascians scripting the entire creation of the Allagan Empire, which certainly helped as well. Xande very well likely had Emet-Selch's help orchestrating the opening act from what the man himself had described. He even said that Garlemald paled in comparison to Allag. The Garleans have no magic, nor even the capacity to wield it. They were only able to fight on equal footing with guns, contracts with voidsent, and Roegadyn battle mage mercenaries. It wasn't until Emet-Selch that magitek took off and they were able to make an empire.
Now think of a world that had just forsaken magic because of its role in the previous umbral era and 1 guy gathers together all the outcast mages. With the power of magic while everyone else has none, there wasn't much in his way and Allag was able to conquer much faster and more efficiently than anything in our world or even the Garleans. Plus, Emet-Selch probably uplifted the magical understanding of early Allag just like he uplifted the science of Garlemald.
What I took was straight from Eorzea Encyclopedia. But just because they were using tomestones at the end of the Allagan Empire doesn't mean they weren't using books a thousand years previously when Xande initially started conquering everything and rebels with eikons were opposing them.
Besides, the section of Allag regarding Aetherochemistry says that the first bits of it were siege weapons and cranes. They had to start somewhere and didn't make airships and computers directly after bashing two rocks against each other. But the empire was founded upon that early combination of magic and machine and it continued ever since.