I'm not sure I've got the question right, but if you're asking what I think you're asking, the basic answer is that we assume a process model, and based on that model, we can derive a PDF.
Keep in mind that this is also true of the probability distribution of a discrete random variable such as the result of a die roll: If we say that a die is fair, this is an assumption we make in order to assert the distribution
$$
p_k = \frac{1}{6} \qquad 1 \leq k \leq 6
$$
and if we say that it's unfair, in such and such a way, that's an assumption we make in order to assert a different distribution. If we're talking about a real physical die, then we can make experiments (roll the die as many times as we like), but even so, we cannot obtain the "true" ideal distribution of the die, since we cannot make an infinite number of experiments.
This is no less a problem than it is with estimating the interarrival distribution of buses at a bus stop. What often happens is that we conduct experiments, sampling the random variable in question, until we have enough data to propose a model distribution. We might say that the distribution is Weibull, with such and such parameters. We can then conduct statistical tests to see how well further measured data matches that distribution, possibly resulting in a refinement of the model, and further tests.
At some point, however, we declare our satisfaction with the model, and use the distribution for whatever our purpose is, such as predicting the expected number of people waiting at the bus stop. At no point do we have a proof that our model is correct (in the same sense that we can prove a geometrical theorem), but it is sufficient for our needs.
