The Hubble Constant
There are two ways to generate the Hubble constant (the rate at which the universe expands) and they disagree. One uses data from the early universe, another from the late universe. Has anyone considered that they might both be right, and the rate was different in the early universe than in the late universe?
In general, if you're not sure what to do, try lots of different things and see which works best. Get different groups of people coming at it from different angles. Most importantly, offer the problem to young mathematicians, physicists, and astronomers who are just entering the field and don't have a dog in the fight yet. They're more likely to find a solution than the old people who already have a strong stance.
And don't worry too much about it. You're not going to understand everything about the universe even after you solve this bit. It's just one more step. An important step, but not everything. It's not worth freaking out because you don't have the answer. You will never have all the answers, and that's what makes it interesting.
In general, if you're not sure what to do, try lots of different things and see which works best. Get different groups of people coming at it from different angles. Most importantly, offer the problem to young mathematicians, physicists, and astronomers who are just entering the field and don't have a dog in the fight yet. They're more likely to find a solution than the old people who already have a strong stance.
And don't worry too much about it. You're not going to understand everything about the universe even after you solve this bit. It's just one more step. An important step, but not everything. It's not worth freaking out because you don't have the answer. You will never have all the answers, and that's what makes it interesting.