Is half inch plywood thick enough for the sides and surface of a ramp? I got some free but most builds call for two layers of 1/4” on the surface and 3/4” for the sides
Thicker is safer for sure.
It also depends on how big the ramp is and how much of a strain is going to be put on it.
For a skatepark that gets all day every day type wear, that thing has to be solid, but for a solo skate lightly in your own backyard type of ramp, I have never had any issues with the sides being about that on most of my ramps I had built over the years.
What I would recommend is also to brace the sides with 2 x 4 pieces as well - same as what I use as the ribs for the transition support, just so it holds up better.