All they actually needed to do is pay attention.

Both Columbia and Challenger were quite preventable, but the problems were basically ignored because they clearly hadn't destroyed the orbiter. Never mind that both showed random behavior outside the design spec, sooner or later the orbiter was going to roll a 1. They had seen the blow-by that killed Challenger, they had seen orbiters scoured by the foam before.

However, it didn't really have a solution. The blow-by problem that destroyed Challenger was fixable, the foam problem was not. You could reduce the chance of a problem but nothing could be done about the fundamental problem of having parts of the heat shield aerodynamically behind other parts of the spacecraft, especially cryogenic parts of the spacecraft. (Ice could also do damage.)