Objections to omnipotence take only two forms: Straw man, and toothless. Omnipotence is often understood by the uneducated as the complete absence of limits. God should, in their minds, be able to do literally anything, even if it is illogical. A round square, for example, should be entirely possible for God to create.
Now, in Christianity, this is nonsense. There are several things God cannot do, such as deny Himself (2 Timothy 2:13). The creation of a round square certainly falls into that category. Ultimately, in Christianity, omnipotence is not the complete absence of limits, but the absence of external limits. The only limit on God is God. He cannot deny Himself, but He can deny anything that isn't Himself. If He wants to create a universe, He can create a universe. If He wants to cause miracles in that universe, He can cause miracles in that universe. But there are some things God cannot do simply because they are not Godly things to do.
The way I like to explain this is by describing my own abilities. What do I mean by the phrase "I couldn't kill a baby"? Obviously, killing a baby is well within the abilities of just about any living adult. If I wanted to kill a baby, I could. But why would I ever want to kill a baby? The very thought of it is sickening. Thus, in that sense, I cannot kill a baby. In much the same way, God may well be physically capable of doing many things that the Bible explicitly states He cannot do.
But many atheists twist the idea of omnipotence to the point where God should, by their reckoning, be able to do literally anything, even the things scripture says He can't do. Of course, the simplest thing to do here is point out the above. If you are using that definition of omnipotence, you are creating a straw man. Suffice to say, this is seen as silly at best, and outright unethical at worst. So, the simplest solution should be to expose the straw man, forcing any rational atheist to retract their objection. The problem? Rational atheists are a minority. Most atheists, at least in my experience, double down on the straw man.
Ironically, however, this produces a sick solution. I say sick because it is an abomination to Christianity, but it is actually far simpler than the actual answer. If we use the real solution, we can talk about how God's limits on Himself are not in conflict with His omnipotence, but if we accept the straw man definition of omnipotence, then God's ability to do the logically impossible means He can actually do the logically impossible. That means all objections to His omnipotence fail in a way no Christian ever wants them to! Can God create a box He can't look into? Yes, but He can still look into the box. Contradiction? Yes, but you just defined His omnipotence as the ability to contradict Himself! Problem of evil? Gone in a puff of smoke. God can be 100% evil and 100% good, at the same time, in the same sense, and there's nothing you can do about it, because you basically said He can contradict Himself.
We told you not to do it. We warned you it was a straw man, we begged you not to make a fake version of our God, but you did, and when we asked you to stop, you doubled down, and now your fake version of God is easier to defend against your nonsensical objection than the real God, because whereas apologetics requires intelligent thought, your straw man requires as much thought to respond to as you put in to creating it, and that is to say none!
So take your pick, atheists. Do you want to reasonably discuss the actual version of omnipotence, as presented by the Bible, which will ultimately lead to you realising that you cannot contend with God on this front? Or do you want to play stupid games, winning the stupid prize of looking uneducated by trying to refute an imaginary God that also happens to be irrefutable? Please, please, please, choose the real God, because when we talk about Him, we can eventually get to talking about the impossible thing He has done for you: Bought you eternal life.
As sinners, it is impossible for us to get to Heaven. We messed up, we stored up God's wrath for ourselves by rebelling against Him. We simply could not be redeemed to Him. But because He is omnipotent, He found a way: Penal Substitutionary Atonement. Either the finite being can suffer the eternal punishment for sin, or the eternal God can suffer a finite punishment for sin. God chose the latter. 2,000 years ago, Jesus, the Son of God, was incarnate in human flesh. He lived a perfect, sinless life, which ended with the turmoil of the cross, where He died. He died for the sins of the whole world. Because of this, we can effectively "swap verdicts". Jesus, who was innocent, was judged as if He was guilty of your sins. Thus, you can be judged as if you were innocent, as He was. There is one condition: Faith. Believe that He is the risen Lord, and you will receive eternal life. The alternative is the second death. Eternal punishment. God has made His choice: He wants you to live. Do the smart thing and obey.