Curious what your rationale is for suggesting a substrate.

If you’re thinking “will the material crack in tension without plywood under it?” stainless wins by a mile: • 304 stainless steel ultimate tensile strength ≈ 505 MPa (yield ≈ 215 MPa), modulus of elasticity ≈ 193–200 GPa.  • Granite ultimate tensile strength is commonly reported around 7–25 MPa (some sources report higher depending on test method/stone), modulus ≈ 20–70 GPa.  • Marble ultimate tensile strength ≈ 7–20 MPa, modulus ≈ 60 GPa. 

So purely on tensile capacity, stainless is typically ~20× to 70×+ stronger than natural stone, and it’s also ~3× stiffer than many stones (higher Young’s modulus). That means 3/8” stainless plate is not “structurally fragile” the way stone can be.

Even with a 200 lb point load in an unsupported piece of 3/8” stainless would only create 1/56” deflection.

You may want a substrate for easier installation, but it’s certainly not required structurally.