I am of two minds with Azem. I of course am curious how they were and what they have done but at the same time I am like: Would it matter?

Even if they did search for another way they failed. They failed because history is as we know it is. (I guess one could argue that this would at least prove that these two ways with Zodiark and Hydealyn were the only solutions but even Azem is not all-knowing)

I also doubt that they just casually had a time machine. (Emet was really curious about the time traveling that Graha had done) In my mind Azem probably tried to save as many people from outside Amaurot as they could. No bigger evil, no plan to stop whats coming, just them going around helping as many people as they could.