The lorebook is probably the best source of information is the least biased version. Your best bet is to look at the Timeline of the 6th Astral Era and do some math with dates. As for the info in the lore book...

The Garleans were originally in southern Othard, probably around where Dalmasca is now.

They were gradually forced northwards, mostly because they couldn't keep up with the magical arms race of all the other races. It should be mentioned that around a third of the "Garlean Population" is actually not racially Garlean at all. So a third of the Cultural Garleans can use aether just as well as everyone else can. What is not known is if the Garleans were specifically discriminated against because of their race or if they just couldn't have a fair fight with other nations because most of their population was at a magical disadvantage.

That northward migration happened over 700 years ago. It ended when the Garleans got to Northern Ilsabard and didn't have anywhere else to go. They eventually found ceruleum and used it as a fuel source and founded their first northern cities. In 922, the northern Garlean cities finally banded together to create the Garlean Republic. The Garlean Republic would last for 600 years. During that time, they would successfully defend their land from invaders, weather that be through subterfuge or conventional warfare. It was pretty obvious the Garleans were in northern Ilsabard to stay.

The Republic ended when a Legatus named Solus Galvus introduced magitek to the military, which turned the tables on Garlemald's enemies. Now Garlemald was winning the magitek arms race. Solus began conquering the nations surrounding the Garlean Repbulic and eventually declared himself Emperor and took over the Republic. Garlemald was now an Empire.

Ever since then, Garlemald has steadily expanded it's borders, almost always though military might.

So yeah, the Garlean homeland has been Northern Ilsabard for over 700 years. And they had one of the longest running stable democracies in the Three Great Continents (only older democracy is Sharalayn). And then for some reason (looks at Solus), they go off on a conquering spree. It kinda makes you wonder why they didn't try to do that earlier; they've had plenty of time to do so.