"remote time" is correct and usable in written English.
It can be used to refer to a time that is far in the past, distant, or far removed from the present. Example: The ruins we visited today were from a remote time, dating back to the ancient civilization that once inhabited the area.
Many stations moved it to more remote time periods.
Two of the board members were overseas, dialling in from remote time zones.
Nor, to this reader's disappointment, does his tour of his boyhood neighborhood encounter any human survivors of that remote time.
Although John Sayles's new film, "Amigo," is set in what seems to be a remote time and place — a hamlet called San Isidro, in the Philippines, around 1900 — it bridges the gap in a hurry.
Someone has found a relatively easy way to enable remote Time Machine backup to a WHS.
A museum of the past, for this traveler coming from the same remote time.
By mixing parallel personal experience, research and instinct, figures from remote times and cultures can be conjured into life.
Although the origins of most folk performing arts lie in remote times, later court forms exerted important influence on many of the folk forms.
Not that any marvel or preternatural happening taking place in secular (as opposed to biblical) history was necessarily to be believed: it was simply that the remote times and regions were convenient locations for picturesque and marvellous incidents.
For all but the last century of Egyptian prehistory, whose neolithic and later phases are normally termed "predynastic," evidence is exclusively archaeological; later native sources have only mythical allusions to such remote times.
The seeming importance of this regular non-news, on the cover front page might be a better description today presumably contented the minority of money-market boffins among our very few thousand readers in those remote times.
