It's a colloquial usage. Although "since" is redundant, the word "since" is used whenever a specific time is mentioned.
"It has been here since last week."
Consequently, it seems somewhat natural to say "since forever". In addition, because it is obviously incorrect, it often has a joking quality because it is a lie. Nothing has been anywhere "forever" (for an infinite time). So it emphasises an exaggeration.
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