  Inhomogeneous cosmological models are often reported to suffer from a
fine-tuning problem because of the observer's location. We study if this is a
generic feature in the Lema\^{i}tre-Tolman (LT) models, by investigating if
there are models with freedom in the initial state. In these cases, the present
fine-tuned location would be evolved from a non-fine-tuned initial state and
thus vanishing the problem. In this paper, we show that this is not a generic
problem and we give the condition when the LT models do not have fine-tuned
initial state. The physical meaning of this condition, however, requires more
investigation. We investigate if this condition can be found from a special
case: homogeneous models with matter, dark, and curvature density as
parameters. We found that with any reasonable density values, these models do
not satisfy this condition and thus do not have freedom in the initial state.
We interpret this to be linked with the fine-tuning problem of the initial
state of the homogeneous models, when the early time inflation is not included
to them. We discuss of the condition in the context of non-homogeneous models.
