Here's the question. Does it literally say that or is that what you think the text implies?
There's not a whole hell of a lot said about Galadriel in general, and even less that the show has to work with. From the LotR appendices, we know she's counted as one of the 3 greatest of the Eldar, which is why she bears a ring (the others being Gil-Galad and Círdan). We also know that she's the one who throws down Dol Guldor with her power. So we know she's formidable. But beyond that, we have little that is concrete for the show to go on without dipping into other sources that are off limits.
"First Age
Once in Beleriand, she lived nominally with one of her brothers, most likely Finrod, but
spent much time at the court of Thingol and Melian in Menegroth, where she arrived in FA 52 and was welcomed because of her family relationship to Thingol's brother Olwë, Galadriel's maternal grandfather. She met Celeborn, a kinsman of Thingol, in Doriath. She also traveled to visit her brother, Finrod, in his realm of Nargothrond multiple times. Her three other brothers were killed during various battles in the First Age.
Galadriel became friends with Melian the Maia, who wanted to know the cause of the Exile of the Ñoldor. Galadriel only briefly narrated the story to her, leaving out the death of Finwë, the Kinslaying at Alqualondë, and the burning of the ships at Losgar. She dwelt in Nargothrond with her brother Finrod, and asked him if he would take no wife. But Finrod had taken an oath only for himself, and his beloved had been left in Valinor.
She had no role in the major wars of the First Age, believing that defeating Morgoth was beyond the power of the Eldar; when Morgoth was defeated by the coming of the Valar out of the West she, having played no part in the earlier Kinslaying, was offered safe return to Valinor. However, she chose not to leave Middle-earth, and was the only leader of the Ñoldor exiles to remain after the First Age."
She spent most her time in the first age living in security, talking with Melian and taking no role in the major wars of the first age.
"Second Age
Celeborn and Galadriel traveled first to Lindon, where they ruled over a group of Elves as a fiefdom under Gil-galad, the High King of the Ñoldor. Sometime later, they had a daughter, Celebrían. They moved eastward and established the realm of Eregion, or Hollin, which they ruled under Gil-galad. Eregion, to the west of the Misty Mountains near Khazad-dûm, was a prosperous kingdom during this time, and had open trade with the Dwarves. Also, during this time, they made contact with a Nandorin settlement in the valley of the Anduin, later to be known as Lothlórien. Subsequently, when Celebrimbor took over the rule of Eregion, Galadriel left by way of the mines of Khazad-dûm. After the death of King Amdír, in the War of the Last Alliance, and the departure his son Amroth, Celeborn and Galadriel became the Lord and Lady of Lothlórien."
In the second age she settled into being a ruler, then left to go to Lothlorien. No wars or battles.