I imagine everything in the immediate area will become Swiss cheese within a matter of minutes. After an hour you'll be hard-pressed to find any surface materials within a kilometer of the ark-ship. I imagine by the end of the day the entire safe zone will look like a carpet-bombed beach-head from World War 2.
As for me? The first thing I'll do is familiarize with the ore scanning tools and try to become proficient to a useful degree, and go for the deeper materials right at spawn, wasting no time on travel, as they will be largely undisturbed by everyone head-set on a gold-rush above. Whilst everyone will be stripping away topsoil and hauling away from spawn to look for materials elsewhere, I'll be patiently gathering rare deeper materials right at spawn, having wasted no time exploring for a safe alcove to set up in the wilderness. That is, if the "rare" materials found at spawn are sufficient to advance and manufacture a craft capable of leaving the planet.