I think the best man-made swimming pond beach is probably a concrete slab. It's durable, cost efficient, and easy to maintain.

For around $300 (along with about a gallon of sweat equity) a sturdy 12' x 12' x 3" DIY slab can be built using approx 60 bags of ready mix, 300' of 3/8" rebar, and a few 2x4's.

A simple broom finished slab covered with a few inches of coarse river sand can make for a rather comfortable and clean beach

If I were to build one I'd go much bigger than 12' x 12', and to save on the sweat equity I'd definitely use truck delivered concrete.