The world Fullmetal Alchemist is set in is not only not the same as ours, but it's also set on a different timeline. Despite the historical resemblance, you need to think of Amestris and the other countries as a whole new universe, in no way related to our own. Except for some confussing obscure Great Britain reference, our world is not mentioned at all during the series.
This timeline is based only in the timeline included in the Perfect Guidebook 2 and translated partially by ZOMGFTA. Go there for a more detailed one.
before recorded history
Country of Xing is founded.
Country of Amestris is founded.
Collapse of the city of Xerxes.
Pride is brought to life by Father.
Lust is brought to life.
more than 200 years earlier
Greed is brought to life.
Envy is brought to life.
Sloth is brought to life.
Gluttony is brought to life.
about 100 years earlier
Greed disassociates himself from Father.
60 years earlier
Wrath is brought to life.
1885
Roy Mustang and Maes Hughes are born.
about 20 years earlier
Wrath (King Bradley) is appointed to office of Fuhrer of the military.
The country of Amestris battles with bordering countries one by one and begins to gain territory.
Hohenheim and Trisha meet, then start living together.
1899
Edward Elric and Winry Rockbell are born.
about 15 years earlier
Ling Yao is born.
1900
Alphonse Elric is born.
1901
Outbreak of the Ishval Rebellion.
about 10 years earlier
Hohenheim leaves home.
Trisha passes away due to a plague.
1908
Beginning of the Ishval Massacre. National Alchemists become involved. Mustang, Hughes, Armstrong, Hawkeye, Kimbley and others partake in the war. Marcoh goes missing.
The Rockbell couple is killed in Ishval.
In the summer, Edward and Alphonse are taken in as Izumi's apprentices.
In the winter, Edward and Alphonse finish their training and return to Resembool.
1910
Edward and Alphonse fail at performing human transmutation.
Mustang recruits Edward.
Edward is equipped with automail.
1911
In October, Edward acquires national qualification.
On October 3, the Elric Brothers burn down their house.
1913
At Central headquarters, the Fullmetal vs Flame mock battle takes place.
1914
Scar begins his attack on the State Alchemists.
Main plot begins.