As other posters have mentioned, yes, large stumps, rocks and huge driftwood work as anchors. But, of course, those things are rarely positioned for all four corners of your shelter. So here's what you do: deadman anchors.
As you approach your camping site, start gathering sturdy sticks. 1"+ in diameter. one to two feet long. As many as you need tie-down points.
Dig a trench perpendicular to the direction of pull. Bury the stick with your tent guyline around it. Better yet, bury it with a small loop of cord so that the loop projects above grade. You want the cord attached in the center of the stick.
You can create a more substanial anchor in this way than ANY tent peg. To secure raft on the Colorado river, I've buried an 8-foot log. The log can't move without moving the 1000 pounds of sand in front / above it.
If truly devoid of modest-sized sticks, get creative. A series of small sticks works. A long stretch of rope works, although big knots in it will help. (not suggesting you BRING the long rope, but on my beach, I find commercial fishing gear all the time). You could even rig up monofilament to buried pop bottles and beer cans to create an anchor. A pot or stuff sack fill of sand and buried is going NOWHERE.
Slightly moist sand is much more cohesive than dry sand. Presumably at a beach, you have an infinite source of water with which to make moist sand.
This is an engineered anchor, but imagine it with a stick and light cord, recovered with soil/sand: 
