From the author's perspective, Galadriel was a late addition to the "stable" of Finwe's line. She was added in while LoTR was being written. Once the decision was made to have her be the daughter of Finarfin, she obviously had to survive the First Age.
Tolkien grappled with this issue in various versions. One has Galadriel meeting Celeborn in Valinor and the two of them planning to take ship to the East when the rebellion occurred. Another has her fighting on the side of the Teleri in Alqualonde. In either construction, her rebellion is less "serious" than the transgressions of her kin.
There are also multiple versions of what happened to her in Beleriand. One has Galadriel and Celeborn departing into the East early in the First Age under the belief that the war against Morgoth was futile. This is consistent with FoTR in which she says that she and Celeborn departed from Beleriand before the fall of Nargothrond or Gondolin.
The second has her residing in Doriath until its fall, after which she presumably passes into the East with her husband. The version discussed earlier has her departing before the defeat of the Noldor, explaining her survival. The latter does not explain her survival other than that she was not slain.
Though she lived, she was not free from misfortune. Her brothers, uncles, aunts and cousins all died in Beleriand. If she dwelt in Eregion as some versions say, that realm perished as well and the Mirdain may have rebelled against her. In any case, she fought the "long defeat" and stayed while her people diminished. If Amroth was her son as some versions suggest, he died as well and her daughter was imprisoned and tortured by Orcs. She had her share of sadness.
In addition, she may have been barred from the West as a result of her participation in the rebellion, though this is also subject to interpretation. Either way, she was meant to stay in Middle Earth by exile or choice. To some extent, her roles were fated and she was meant to survive in sorrow as all around her fell or diminished.
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Beleriand, Beleriand,
the borders of the Elven-land.
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