Directory of Prototype block files. Maine is state 23, Kennebec is county 11. The zip file is for the entire state, but I haven't found a shortcut to get county specific files.
1) Go to
http://www.census.gov/rdo/ .
2) Under "Recent News", click on "2020 Census Program Phases"
You probably have been to this page, which has a lot of information about the BBSP and guides for using both their GUPS (the one you said was built over QGIS) and your own software. But anyway, ...
3) Under "Phase 1 - Block Boundary Suggestion Project", under "Geographic Files", click on "Partnership Files" (note the "(use 2016 Partnership Files)" right after that hyperlink).
4) Select your preferred vintage (2015/V1 or 2016/V2 (I did what they said to and downloaded the the 2015 shapefiles for Maine, but only the statewide ones and those for Kennebec and Aroostook because of how big it all was; I had already downloaded the prototype block shapefiles for every Maine county).
5) Select your desired state and click "GO".
6) You can batch download up to five counties' shapefiles at a time. For each batch download of 1-5 counties there will be a folder for both Maine and each county in that batch download.