Could science be lost if a phenomena is observed before predicted?
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.