In conversation many native speakers would use present perfect and many would use simple past in that scenario:
I don't recognize that shirt you're wearing.
--Really? I've worn it many times before.Is that a new shirt?
--No, I wore it before.
Some would even say
I've wore it before.
which is considered substandard; the standard past participle of wear is worn.
I suspect the use of the simple past there, with before, would correlate with a lower than average "grade reading level" or with a person who had grown up in a milieu where the grade reading level was lower than average.
But before in this context does not mean "a moment ago", contrary to what you say in your question. It means "prior to now".
I've never seen anything like it before.