How it doesn't fit
First, here is how the Russian Invasion DOES NOT fit, into End Times Prophecy. Contrary to a lot of teachers of Bible prophecy (especially contemporary ones), this invasion is not a precursor to the fulfillment of Ezekiel 38. There are several reasons for this (and I have included them in this paper on Ezekiel 38 and 39), but one key indicator is that, in Rev 20:7-10, the Apostle John seems to link Ezekiel 38 with the invasion of Israel which occurs at the end of the Millennial Kingdom (the thousand-year reign of Jesus, following His return to the earth).
How It Might Fit
Here is how I see the invasion of Russia into Ukraine possibly fitting into Bible prophecy. Russia currently has a toe-hold in the Middle East via links with Syria and Iran; in fact, Russia currently has military troops in Syria which is a threat to Israel. If Russia’s invasion into Ukraine puts too much strain on Russia’s economy, on Russia’s military, and on Putin’s standing as the dictator of Russia, Russia may be forced to pull its forces out of the Middle East. That would leave Syria, which is being propped up by Iran, and Iran as two nations standing alone against the rest of the Middle East states.
Then, if (perhaps “when,” not “if”) Israel finally launches a necessary preemptive attack upon Iran, one that the Lord uses to bring down the current Iranian regime (perhaps the Iranian Green Movement would use the resulting chaos of that attack to launch a government coup), then, in all likelihood, the current Syrian regime would also collapse. This result would open up the Middle East for negotiations on the Dan 9:27 treaty, the treaty that starts the clock ticking on the seven-year tribulation period.
In my view, ten national leaders will be involved in confirming that seven-year treaty with Israel. [These are the ten kings of Daniel 7:24 and Revelation 17:12.] I believe five of these will be leaders of Middle East states, while five will be leaders from European nations.
In addition, the Biden administration is planning to use Russia as a prime negotiator in the Iran deal, which would enhance Iran’s ability to access nuclear weapons, enrich Iran financially, and provide Russia a backdoor to escape economic sanctions. This deal would threaten Israel and the entire Middle East, as well as the United States, and would threaten a future Middle East treaty with Israel.
Thus, I believe God may use the Russian invasion of Ukraine to overly stretch Russia, which could likely result in Russia pulling out of the Middle East and threaten its part in the U.S.-Iran deal, thus cratering that deal. This, in turn, could be one part of the recipe for preparing the Middle East for the Daniel 9:27 treaty.