Lush greenery beneath a big tree may be a tall order. Do any weeds grow there? If not that’s an indication of the challenge. It may be a question of trial and error. Can you show a picture of the area?

btw, if you leave the fallen leaves you won’t have just dirt.

I would plant hosta. Smaller varieties and keep well watered. While oaks give pretty dense shade their roots go deep and hosta do well beneath them.

Hostas are out if deer are a problem.

And I’d be reluctant to plant anything that needed watering in perpetuity.

Hostas do fine under my oaks. Mitchella Repens, partridgeberry is often found close to trunks of trees.