Does Allah (SWT) truly forgive an ugly deed and a major sin committed by a girl in her youth, knowing that she has repented for it and cannot forgive herself, and has lost hope in life because of it?

Adultery (zina) is one of the grave sins, and its preliminaries are forbidden. It is even more severe when committed with maharim (unmarriageable kin). If a servant repents, Allah accepts his repentance, for Allah is Most Forgiving, Most Merciful; He forgives all sins, no matter how great. Whoever seeks His forgiveness will find Him Most Forgiving, Most Merciful. Increasing acts of seeking forgiveness (istighfar) and striving in obedience to Allah expiate evil deeds.