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.)

The shuttle needed extensive refurbishment between flights. It wasn’t until after the loss of Columbia that they examined heat shield damage in orbit, assuming any damage observed on the ground would have occurred during reentry. For an organisation so risk averse as NASA, I was surprised how little focus was placed on the orbiters as experimental vehicles.

The external fuel tank, whence came the foam that stuck the wing, leading to the loss of Columbia.