Huh? How is it necessary to speak of time when discussing whether there exists e.g. a solution to a set of equations?

Or whether there is a finite simple group with given number of elements, or the like?

Does the solution to an equation exist before one stated the equation? Does a particular phrase exist before one has written it? Does it continue to exist after all its copies were erased? And even if one answers positively to such questions based on a belief (it is not provable), like "yes, they always exist", one has to define what "always" means.

Their existence is not at all dependent on such things. (Note that I didn’t use the word “always”.)

If the answer to a question of “Why [...]_1?” would be “Because there is a [...]_2 such that [...]_3 .”, then there is such a [...]_2 such that [...]_3 . (Possible exception : if “because you asked that question” would be part of the answer.)