I would really like to advice you again not to go any further down the line on this family until you know for sure that the Sven Gustaf I found is your Charles Freeberg. The name change is just too great without a confirmation or some indication from the US records.

I did however look into what you found. You would need to follow the trace from the birth records onto the censuses, then keep searching through each book/year but this is where it changes from "just" Gustaf to Sven Gustaf
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Adelöv AI:13 (1851-1859) Bild 124 / sid 101 (AID: v18745.b124.s101, NAD: SE/VALA/00001)

Gustafs mother has married

Anders Magnus Johansson, b. 26 JUN 1816 in Adelöv, Jönköpings län, Småland
Maja Stina Johansdotter, b. 19 DEC 1924 in Ödeshög? Died 13 DEC 1856

Her children
Gustaf, b. 22 JAN 1847 in Adelöv, Jönköpings län, Småland
Kerstin Sofia, b. 18 MAY 1850 in Adelöv, Jönköpings län, Småland. Died 25 MAR 1856

Their children
Carl Johan, b. 5 SEP 1853 in Adelöv, Jönköpings län, Småland
Maria Christina, b. 24 FEB 1855 in Adelöv, Jönköpings län, Småland.
Victor Alfred, b. 10 JUn 1858 in Adelöv, Jönköpings län, Småland. Died 3 FEB 1859
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Adelöv AI:14 (1860-1865) Bild 210 / sid 184 (AID: v18746.b210.s184, NAD: SE/VALA/00001)

Widower Anders Magnus Johansson, b. 26 JUN 1816 in Adelöv, Jönköpings län, Småland

Maja Stinas son
Sven Gustaf, b. 22 JAN 1847 in Adelöv, Jönköpings län, Småland

Their children
Carl Johan, b. 5 SEP 1853 in Adelöv, Jönköpings län, Småland
Maria Christina, b. 24 FEB 1855 in Adelöv, Jönköpings län, Småland.

So this is the first time the name Sven appears.
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Anna