This is basically an issue with all "fine tuning" type problems that show up in modern physics. There is nothing mathematically wrong with initial conditions where the matter density is initially uniform. And it is a defensible position to say that it doesn't mean anything to say that one mathematically possible set of initially conditions is more or less likely than another set. To make a statement like that implies that somewhere you have in mind some probability distribution over the set of all possible initial conditions, and you could argue that this distribution is necessarily a subjective choice so you can't trust any conclusions drawn from it.

The perspective many physicists take, however, (including myself), is that parameters in physics should act as if they were drawn from some random distribution, modulo relationships that we know have to exist between parameters (like certain coupling constants having to be equal because of symmetries). An analogy in number theory is the heuristic random model of prime numbers -- it is widely believed that prime numbers should behave randomly up to patterns that are known to exist. So in that kind of picture, a perfectly homogenous initial condition is very surprising, because a typical draw from a reasonably broad distribution of initial conditions will not anything look like that.

To say it another way, we basically expect there shouldn't be patterns in the Universe unless we have an explanation for why that pattern is there. We don't have a reason to think that the initial conditions should be homogeneous, which would lead us to guess the initial density distribution should just be some arbitrary function, and therefore it's surprising when we find that distribution actually has a lot of structure. As far as we know, it could have been anything, so why did it turn out to be something so simple?

I'm painting a simple picture here, and you could push this discussion very far in lots of different directions -- you could challenge the model of the physical parameters we observe acting like they are drawn from a random distribution since we only ever see one world, you could ask precisely how you define a probability distribution over the parameters and how is such a distribution even defined in some cases, etc -- my point isn't to try to resolve any of those debates, just give some idea of where the intuition behind fine tuning problems comes from.

This is basically an issue with all "fine tuning" type problems that show up in modern physics. There is nothing mathematically wrong with initial conditions where the matter density is initially uniform. And it is a defensible position to say that there's no sense in which one mathematically possible set of initially conditions is more or less likely than another set. To make a statement like that implies that one is using a probability distribution over the set of all possible initial conditions, and you could argue that this distribution is necessarily a subjective choice so you can't draw any rigorous, scientific conclusions drawn from it.

The perspective many physicists take, however, (including myself), is that parameters in physics should act as if they were drawn from some random distribution, modulo relationships that we know have to exist between parameters (like certain coupling constants having to be equal because of symmetries). An analogy in number theory is the heuristic random model of prime numbers -- it is widely believed that prime numbers should behave randomly up to patterns that are known to exist. So in that kind of picture, a perfectly homogenous initial condition is very surprising, because a typical draw from a reasonably broad distribution of initial conditions will not anything look like that.

To say it another way, we basically expect there shouldn't be patterns in the Universe unless we have an explanation for why that pattern is there. We don't have a reason to think that the initial conditions should be homogeneous, which would lead us to guess the initial density distribution should just be some arbitrary function, and therefore it's surprising when we find that distribution actually has a lot of structure. As far as we know, it could have been anything, so why did it turn out to be something so simple?

I'm painting a simple picture here, and you could push this discussion very far in lots of different directions -- you could challenge the model of the physical parameters we observe acting like they are drawn from a random distribution since we only ever see one world, you could ask precisely how you define a probability distribution over the parameters and how is such a distribution even defined in some cases, etc -- my point isn't to try to resolve any of those debates, just give some idea of where the intuition behind fine tuning problems comes from.