Existence must exist at all times.

[Ignorant]

Whatever existence is, I don't need to go into in order to argue that whatever it is it is indeed eternally existent.

Here is my argument:

Existence must always exist because that is the same as existence always being existent. Existence must always be existent for the same reason that atheists must always be atheistic, theists must always be theistic, agnostics must always be agnostic, elephants must always be elephant like, humans must always be human, squares must always be square, circles must always be circular, triangles must always be triangular, etc etc [fill in the blank]. This is the Law of Identity in logic. It is A=A and is never not A.

Because existence is existent at all times, that logically entails that existence, whatever it is, is eternal and never began and will never stop. This is different to the beginning of the universe or the big bang.

The question is never whether existence itself exists, whatever it is it is existent by definition for the reason explained above. The real question is twofold I reckon:

1. What exactly is existence?
2. Is question 1 a pointless question and existence by itself as the totality of all things a rather vacuous concept or is it worth thinking about?

Something about existence (whatever it is) is ontologically necessary and not merely historically necessary (like you said, "this is different to the beginning of the universe or big bang"). "Whatever [existence] is, it is existent by definition", and "that logically entails that existence, whatever it is, is eternal and never began and will never stop".

1) Great question. Do some things "begin" or "cease" to exist or both? In other words, even if the "totality of all things" is continuously and eternally existent, do some things exist discontinuously and temporally within that totality?

2) I think it is a good question worth thinking about.