A thought just hit me: The English phrase ‘terra incognita’ coming from Latin means ‘unknown territory.’ What would a phrase be for ‘before my time?’ Not necessarly ‘before I was born,’ but more in the sense of ‘before my earliest memory’ or. . . ‘unknown time.’
my earliest memory: prima memoriae
before my time: ante diem
before my memory: in memoriam in conspectu meo
unknown time: tunc nescitur
(being no Latin scholar, I take no responsibility for the correctness of these translations which I acquired from “google translate”. 
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I think “my earliest memory” would be prima memoria mea: “prima memoriae” would be “belonging/pertaining to the first memory” but doesn’t specify whose.
I found “ante me est nemini” as well.
‘ante meam memoriam’ is what you want, especially given you want before the earliest memory.
Or are you asking for something equivalent to “in the olden days,” meaning “before I was even born”?
[QUOTE=The OP]
. . . Not necessarly ‘before I was born,’ but more in the sense of ‘before my earliest memory’ or. . . ‘unknown time.’
[/QUOTE]
So, any time predating my earliest memory, whether or not I was alive at the time.
What Vaevictis said, then. Very appropriate username/subject combo.
Thanks, all.