The expression comes from
Psalm 90:10 (King James Version) — Original Hebrew.
The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow; for it is soon cut off, and we fly away.
The much older Latin Vulgate has the "70 years" as: "septuaginta anni", where the first word is clearly "70" without the use of "score".
The even older original Hebrew text has "שִׁבְעִים שָׁנָה" (šiḇʿîm šānâ).
"šiḇʿîm" has "שֶׁבַע" (šeḇaʿ) as its root, and that simply means "seven", again with no use of "score".
The translators of the Authorized Version (KJV) must have decided to use the more poetic "three score years and ten" instead.
Meanwhile, the famous Gettysburg Address by Abraham Lincoln begins with:
Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.
I suspect that it is mostly Americans that use the "three score and ten years" form, subconsciously paralleling Lincoln's "four score and seven years", while the rest of the world uses the King James translation with the embedded "years".