The way to look at the United States is that the U.S. is the Lion that is raised up on its hind feet and given a heart of a man. Russia is the bear with three ribs in its mouth: Lithuania, Latvia, and Estonia (former republics of the U.S.S.R.) The leopard with four heads and four wings is the United Kingdom of England, Northern Ireland, Scotland, and Wales. The fourth Beast is the EU (European Union) having one currency. Note that U.K. does not partake in that one currency.
You say there is no U.S. in Bible Prophecy? The Lion of Tarshish and all her young cubs are the NATO members. And they will be gainsayers when Russia leads Islamdom into invading Israel. They will fear Russia and the Muslims's terrorist retaliations so they shall not defend Israel.
But have not fear, God shall save the day. Just read Ezekiel 38-39. Note this war takes place before the Antichrist comes. The battle Armageddon, on the other hand, takes place at the end of the 42 months of Antichrist/Dragon rule. Hence, be ever ready for the Lord, so that you can watch both wars from the safety of heaven and not from the Greatest Tribulation on earth.
This Gog/Magog war takes place either near the end of this age before the Rapture or else right after the Rapture. One thing that we know is that it takes place around the time of the Rapure. And the Rapture takes place just before the Jews place the foundation for the Third Jewish Temple.