First fix the downspout so that the water stream is slowed.
If it were my area, would just buy top soil and add until it was slightly above grade, to allow for settling. My daughter had a big dip in the area above and around her septic tank. She ordered a load of decent top soil, then we added a bit more after the soil settled. Finally we planted grass over the area. Her yard is clay, the top soil was sandy loam. You can't tell there was ever a dip now some two years later.
Eclectic gardening style, drawing from 45 years of interest and experience. Mostly plant in raised beds and containers primarily using intensive gardening techniques.