Normally we're supposed to agree upon a definition of time before we can discuss its existence, but it always comes down to a dimension in which we can measure the "sequential distance" between two events. This fundamental quantity is called a time inverval. And it's so trivial we use it every day. Even you used the word time about 3 times on this page alone. And putting it between quotation marks doesn't make it any less real.

Saying time doesn't exist would be as absurd as saying "space doesn't exist, hence length doesn't exist".
Yes I know that, but the Twin Paradox sally mentioned only concerns the effect of time dilatation caused by relative velocity.
A clock basically creates a scale in the dimension of time, like you would put a distance scale on a map. So if time would go "slower" or "faster", the scale of the clock has changed without us realizing it. I think this is what you were trying to ask for.