Could science be lost if a phenomena is observed before predicted? An observation could validate the predictions made by a previous theory. If something unpredicted is observed, then a new theory which is compatible with the observation should make predictions which later are confirmed by new observations.

But what if no such new predictions are possible to make? What is the scientific status of a theory which after the fact is only compatible with all data, but which cannot make any new predictions? If it would be considered weak, does this mean that discoveries through observation can actually destroy science?

Is this a valid argument for delaying the construction of better observatories until theories have matured given all existing data? Kind of comparable with the forward planetary protection argument which says that human spaceflight to Mars should wait until it is certain that there's no life there which could go extinct when it meets Earthly life.
The question leaves me confused on how to interpret it.  As some of the comments have noted, observations have routinely predated a theory that (accurately) predicts them.  In astronomy and cosmology this has tended to be the main driving force behind seeking new theories.  Yet I sense a more subtle question concerning how scientists would view a theory that predicts everything so far, but nothing new.

Ultimately I think there is a confusion concerning the typical mantra for adopting a new theory as the main theory for physics/science/whatever: if a new theory doesn't make any new testable predictions, and so can only reproduce what existing theories already predict, then preference is given to simpler and existing theories.  This has nothing to say about a single theory.  It's strictly about multiple theories being compared to each other.  It does not imply that a theory, viewed entirely on its own, that makes no new predictions is undesirable.  It simply means if we're going to replace theory X with theory Y, then theory Y better predict more stuff than X does.  It doesn't care if X does or doesn't predict testable things that have yet to be proven/disproven.