Can you find out what the cumulative distribution function is if you know the random variable X?

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I have a theoretic question on my probability class. Suppose that you know the X random variable. Can you calculate the cumulative distribution function? If not, why not?

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If you know the distribution of X, the cumulative is the integral of its density function. So yes, I can.

If you have drawins from X, you may be able to fit a distribution, so that you get an estimated continuous density function. You may not be able to express the integral in terms of elementary functions (e.g. the cumulative of a normal distribution), but you may have a numerical approximation. So yes, I can.