This is a complicated problem and it has been studied a lot. I don’t think the best option is to reach conclusions starting from scratch. As with any complex topic, we should study a bit the arguments given by previous thinkers, instead of trying to “reinvent the wheel”. The same way, if we find that we don’t understand the functioning of the DNA, the first thing is to read a book about genetics, instead of reaching conclusions without taking into account the information that has been discovered by the people that came before us.
The size of a combox or a post cannot explain all the complexities of this subject, so, if you are really interested, I recommend you to watch the 5 or 6 videos that William Lane Craig has produced about this topic, where he analyzes all the different perspectives and versions of the problem of suffering. This is the first one:
https://www.youtube.com/watch?v=kMOKakXm1Wc
(and then you can watch the next ones)
I will only say two quick things:
1) My dog thinks I am cruel when I vaccinate him. He can’t imagine that I have good reasons to inflict this suffering. Lack of imagination is not a proof, especially when thinking of someone infinitely more intelligent than ourselves. (And don’t forget that even the worse sufferings of this world pale against the eternal infinite bliss that is heaven)
2) I don’t think “omnipotent” means what you think that it means. In Christianity, “omnipotent” does not mean “God can do everything” (such as Allah in the Quran, see Surah 22:6 and Surah 46:33) but “God can do every thing that is not logically impossible” (this is the understanding of the Bible and all Christian thinkers from Christ to our days).
God cannot create a squared circle (a logical impossibility). God cannot lie (Numbers 23:19, Hebrews 6:18) because lying would be against God’s nature, which is truth (so God’s lying would be a logical impossibility, like a squared circle). God cannot deny himself (2 Timothy 2:13) and cannot be tempted by evil (James 1:13).
In a universe with billions of creatures with free will, lots of things cannot be done by God because they are logical impossibilities. Not only the obvious ones (such as preventing Hitler from killing people while giving him free will at the same time). But also lots of non-obvious ones, because billions of people practicing their free will can cause lots of chains of consequences. And this is only about material causes, without mentioning the logical impossibilities derived from spiritual causes (which we may know or may not know).
But these are only two small comments. For a more detailed analysis of the topic, you can see the William Lane Craig’s videos. And then, reach more informed conclusions.