Yes, they can. There are two main venues for victims of sexual abuse to seek financial compensation, and two venues are available in both cases involving adults and cases involving children. Victims can get financial compensation as a result of a criminal lawsuit, and as a result of a civil lawsuit.
It’s usually easier to pursue a civil lawsuit after the criminal case is done and the abuser has been convicted. And at the end of a criminal lawsuit, the court may order the perpetrator to pay financial compensation for the victim.
If the abuser was some sort of authority figure working for a bigger institution, then the victim can enlist the help of an adult abuse lawyer to file a civil lawsuit against that institution and potentially get financial compensation from them. As this website explains, the authority figure can be anyone from a teacher to a priest or even a park ranger, as long as it can be proven that the institution was neglectful in letting the abuser get and maintain a position of authority despite their bad behavior.