Did God grant Mao, Stalin, and Hitler power?

Yes.  Kermit the Fort sang It ain't easy being green and could have added, But its tougher being Christian (because what one is constrained to confess seems insane to others).

Now, it doesn't mean that Christians have to acquiesce in or succor such a government and the Christian can use every natural law/moral means necessary to change the government controlled by such men but it does mean that God did grant those wicked men power.

City of God, St Augustine, Book 5: Chapter 19.— Concerning the Difference Between True Glory and the Desire of Domination.

...

But it was Nero Cæsar who was the first to reach the summit, and, as it were, the citadel, of this vice; for so great was his luxuriousness, that one would have thought there was nothing manly to be dreaded in him, and such his cruelty, that, had not the contrary been known, no one would have thought there was anything effeminate in his character. Nevertheless power and domination are not given even to such men save by the providence of the most high God, when He judges that the state of human affairs is worthy of such lords. The divine utterance is clear on this matter; for the Wisdom of God thus speaks: “By me kings reign, and tyrants possess the land.” Proverbs 8:15 But, that it may not be thought that by “tyrants” is meant, not wicked and impious kings, but brave men, in accordance with the ancient use of the word, as when Virgil says,

For know that treaty may not stand

Where king greets king and joins not hand,

in another place it is most unambiguously said of God, that He “makes the man who is an hypocrite to reign on account of the perversity of the people.” Job 34:30 Wherefore, though I have, according to my ability, shown for what reason God, who alone is true and just, helped forward the Romans, who were good according to a certain standard of an earthly state, to the acquirement of the glory of so great an empire, there may be, nevertheless, a more hidden cause, known better to God than to us, depending on the diversity of the merits of the human race. 

Book 5; Chapter 21.— That the Roman Dominion Was Granted by Him from Whom is All Power, and by Whose Providence All Things are Ruled.

These things being so, we do not attribute the power of giving kingdoms and empires to any save to the true God, who gives happiness in the kingdom of heaven to the pious alone, but gives kingly power on earth both to the pious and the impious, as it may please Him, whose good pleasure is always just. For though we have said something about the principles which guide His administration, in so far as it has seemed good to Him to explain it, nevertheless it is too much for us, and far surpasses our strength, to discuss the hidden things of men's hearts, and by a clear examination to determine the merits of various kingdoms. He, therefore, who is the one true God, who never leaves the human race without just judgment and help, gave a kingdom to the Romans when He would, and as great as He would, as He did also to the Assyrians, and even the Persians, by whom, as their own books testify, only two gods are worshipped, the one good and the other evil — to say nothing concerning the Hebrew people, of whom I have already spoken as much as seemed necessary, who, as long as they were a kingdom, worshipped none save the true God. The same, therefore, who gave to the Persians harvests, though they did not worship the goddess Segetia, who gave the other blessings of the earth, though they did not worship the many gods which the Romans supposed to preside, each one over some particular thing, or even many of them over each several thing — He, I say, gave the Persians dominion, though they worshipped none of those gods to whom the Romans believed themselves indebted for the empire. And the same is true in respect of men as well as nations. He who gave power to Marius gave it also to Caius Cæsar; He who gave it to Augustus gave it also to Nero; He also who gave it to the most benignant emperors, the Vespasians, father and son, gave it also to the cruel Domitian; and, finally, to avoid the necessity of going over them all, He who gave it to the Christian Constantine gave it also to the apostate Julian, whose gifted mind was deceived by a sacrilegious and detestable curiosity, stimulated by the love of power. And it was because he was addicted through curiosity to vain oracles, that, confident of victory, he burned the ships which were laden with the provisions necessary for his army, and therefore, engaging with hot zeal in rashly audacious enterprises, he was soon slain, as the just consequence of his recklessness, and left his army unprovisioned in an enemy's country, and in such a predicament that it never could have escaped, save by altering the boundaries of the Roman empire, in violation of that omen of the god Terminus of which I spoke in the preceding book; for the god Terminus yielded to necessity, though he had not yielded to Jupiter. Manifestly these things are ruled and governed by the one God according as He pleases; and if His motives are hid, are they therefore unjust?