Back during Apollo, they relit the lunar transfer stage engines in orbit, and just pointed it so it would escape earth and go into deep space.

This also allowed them to have the stage fueled, without risking a giant explosion if it entered the atmosphere. Because the stage was already in a stable orbit, even if the engine didn’t light, all of the fuel would boil off before it entered the atmosphere.

A suborbital flight would only allow a short term test, whereas the real HLS will be spending many days between relights. Plus, the ship will be entering the atmosphere with a substantial amount of fuel in the tanks, which just seems needlessly dangerous.