The present moment isn't going anywhere anytime soon or later.The present moment will go away when the next moment arrives.
Yep, by definition, it will never exist.You state in the following paragraph that the past doesn't exist;
Fallacy of Begging the Question and the Non Sequitur.if that's so, then the present moment will cease to exist once it becomes the past.
The present doesn't become anything. You're mixing contradictory ideas together. The past and future are not the present. Being and becoming are likewise not equivalent either.
Existence is eternal. There can be no beginning or end to existence without venturing into contradiction. If I say that existence doesn't exist, I'm contradicting myself. If I say nothing exists, I'm contradicting myself. By definition, nothing doesn't exist.
I'm not suggesting or equating what exists with existence though. Things may have a beginning or end, and existence is a thing, but it is also a verb, e.g. "be-ing".
Those who assume the existence of time, will inevitably assume that there must be some time before the beginning of time or after the end of time. This is incoherent nonsense. There can be no time before the beginning or time, or after the end of time.
Ultimately, time only exists within the concept itself, and concepts don't exist as anything other than concepts.