Can ice sheets build up over days?

NASA: No. The major ice sheets over North America at the peak of the last ice age took tens of thousands of years to build up.

NSIDC: What can happen abruptly in climate change are shifts in air and ocean circulation. Ice sheets and ocean thermal changes require longer to adjust. When climate changed abruptly during the end of the last ice age, air and ocean currents shifted. In the decades and centuries that followed, these changes gradually affected the ice sheets and deep ocean. Ice sheets that were in equilibrium with the previous ice age climate were not compatible with the new climate; or, conversely, cool areas in northern Canada or Scandinavia that had been ice free began retaining a layer of snow through every summer. Slowly, over centuries, ice sheets grew, or retreated, in response to the climate changes.

This process of shifting climate and changing ice sheets is happening today. In the Antarctic Peninsula, climate has warmed to the point where ice shelves that were stable there for many centuries are no longer stable. The northern most limit for ice shelves has moved south over the past two decades by about 100 miles. (note that ice shelves respond to climate change more rapidly than large ice sheets)