Maybe the smallest way to start (other than growing in containers, pots and (EarthBoxes) is a small raised bed with a hard floor to keep tree roots out.
Creating a lot of soil from clay or duff takes time and energy and probably money. Clearing a spot of shade and tree roots takes at least time and energy.
But if you have pots and plenty of time and energy, you could "follow the Sun" with your pots for the first year.
You COULD move them twice each day to get more sun than any one spot would have gotten. Obviously, this won't work with vines like peas, beans and tomatoes.
When the morning sun moves and starts to shade the pots, move them to where the afternoon sun will be strongest. Then, in the evening, move them back to where the early-morning sun will be strongest.
If you hate cutting down trees, but really want home-grown vegetables, one year of dragging pots around twice per day might help reconcile you to creating some firewood!