The problem of evil is something of a troubling issue for Judeo-Christian-Islamic mythology, and it also stands as one of the more common arguments used by atheists to raise doubts against the theist position. To be honest, I do think a lot of atheists misuse this argument, or at least fail to follow through on it properly. A lot of times, you tend to see Epicurus' famous quote which concisely essays the argument or something along the lines of bringing up a minor counterexample and declaring checkmate. Really, the problem of evil (or its corollary, the problem of suffering) does not actually have the power to disprove a god, nor does a "solution" to the problem have the capacity to prove it. Rather, the attack that the problem of evil poses is that it undermines the logical consistency of the theology itself, which at best shows that if there is a god, it's not the god of particular religion X. Theodicy, for those who aren't familiar, is basically an entire field of philosophy dedicated to the defenses against the problems of evil/suffering which aim to show that a theistic belief system can still be consistent with the existence of evil in the world.
Notably, I did limit myself to Judeo-Christian-Islamic mythology here. For a lot of older religions, there really is no "problem" of evil/suffering to begin with. Hinduism and all of its offshoots (e.g. Buddhism, Jainism, etc.) have concepts of reincarnation and karma which explain evil/suffering someone experiences as a result of past evil/suffering they caused potentially in prior lives as well as purporting that in the long run, good and evil, pleasure and pain, etc. come out balanced such that the game of life is a zero sum game. Hellenistic and Norse mythologies tend to imbue their deities with the same character flaws and emotions that humans have, and they rarely ever act in interests other than their own. No one god was fundamentally good or evil in an absolute sense. In short, these religions have no "problem" of evil and/or suffering in the same sense because the presence of evil is something that is expected, making it quite consistent with those theologies. Judeo-Christian mythology, on the other hand, is faced with a problem because its monotheism also means referring to its god in absolutes and infinites. Thereby writing themselves into a corner.
Notably, I did limit myself to Judeo-Christian-Islamic mythology here. For a lot of older religions, there really is no "problem" of evil/suffering to begin with. Hinduism and all of its offshoots (e.g. Buddhism, Jainism, etc.) have concepts of reincarnation and karma which explain evil/suffering someone experiences as a result of past evil/suffering they caused potentially in prior lives as well as purporting that in the long run, good and evil, pleasure and pain, etc. come out balanced such that the game of life is a zero sum game. Hellenistic and Norse mythologies tend to imbue their deities with the same character flaws and emotions that humans have, and they rarely ever act in interests other than their own. No one god was fundamentally good or evil in an absolute sense. In short, these religions have no "problem" of evil and/or suffering in the same sense because the presence of evil is something that is expected, making it quite consistent with those theologies. Judeo-Christian mythology, on the other hand, is faced with a problem because its monotheism also means referring to its god in absolutes and infinites. Thereby writing themselves into a corner.