I'm guessing the adoption took place in Sweden.
According to a page on Family Search:
Adopted and Foster Children
When a child has been given up for adoption or placement in a foster home, one should always search to see if there is a barnhus (children’s home or orphanage) in the area. If so, it is nearly certain that the child was placed by way of the orphanage. Barnhusets arkiv (Orphanage archives) are in many cases preserved and can be searched. In Stockholm, for example, there is the Allmänna Barnhusets arkiv (General Children’s Home Archive) records before 1897 at the Stockholm City Archives (Stockholms stadsarkiv). Records after 1897 remain at the Children’s Home at Runebergsgatan 11. Göteborg, Lidköping, Malmö and Uddevalla have similar institutions. The orphanage district areas begin with the home city and surrounding areas but may include children from other places.
In some cases, the birth mother may have had a significant influence on the placement of the child. Often this involves unwed mothers who make arrangements for the child to be cared for by a relative or friend. But even when arranged by the home, the mother was able to establish certain measures.
In other instances, especially when both parents are deceased and there is no orphanage in the area, it was the church that took charge of placing the child. Details may be recorded in the sockenstämmprotokollen (parish council minutes) . After 1847, children (especially older ones) were auctioned off to the lowest bidder. If the church paid, the transaction should appear in kyrkoräkenskaperna (church accounting books). If the auction was conducted by secular authority, the records would be found in Länsräkenskaperna, Kronolänsräkenskaperna, or the Kronofogdearkiv, all of which are found in landsarkiven (Provincial archives).
It is important to try and follow a foster child (or orphan) through his/her entire growing years. A child may change foster homes several times and occasionally may even be taken back by the mother (or both parents) should they gain the economic and/or social standing to handle it.
So you'll need to find if your great-grandmother was placed in an orphanage prior to being placed with her American parents.