I'd like to be able to access the points of my character after animation, but I can't figure out a way to unpack the geometry from an APEX setup. Is there a way to do this at SOP level?

Just figured it out. You have to throw down an unpackfolder sop first, then throw down an unpack node

I wouldn't expect needing an extra Unpack SOP unless your geometry was already packed. Maybe you're extracting one level higher that you're expecting. A quick way on the Unpack Folder SOP to unpack all the shapes is to use the pattern: /**/*.shp
The "**" bit means to traverse down multiple levels to find matches. See the help for more on that: https://www.sidefx.com/docs/houdini20.0/nodes/sop/unpackfolder.html [www.sidefx.com]