$\pi$ is perhaps the most famous irrational number. We know it contains all decimal digits from 0-9, just by virtue that all digits occur, at least once, within 32 decimal places:
$\pi = 3.14159265358979323846264338327950$ (32 d.p.)
Similar analyses can be applied to other irrational numbers, such as $\sqrt{2}$, $e$ and more. However, there exist irrational numbers that contain only a subset of the digits 0-9.
Searching the first $n$ decimal places of a decimally expanded irrational number is not a robust approach, as some irrational number decimal expansions contain only a subset of decimal digits, until $n$ decimal places, where $n$ may be a number so large that it is impossible to build a computer in this universe that can assist.
Are there any purely theoretical ways to verify the set of decimal digits that an irrational number contains at least once?