Kiddush Levana can be recited as early as the 3rd day of the Hebrew month.
Two scenarios (may have same or different answers):
A. Suppose a person will be hospitalized beginning the 3rd of the month (or some other reason that would make him physically unable to recite it.)
B. A person lives in an area where overcast skies are almost a guarantee. E.eg. fog is an almost nightly occurrence in San Francisco (and IIRC, certain parts of Israel), esp. during the summer. Or, the forecast predicts rain / clouds for the next 2 weeks (perhaps, rare, but, it has happened in NY area numerous times. Meteorologists call it a "stationary front".)
Can a person recite Kiddush Levana early in either of these (or similar) situations?