After you try and open QGIS and get the error, you need to open MacOS "System Preferences" and select "Security and privacy". You should now see an option there to run the program below the "Allow apps download from:" section.
Thought I would provide an update as the earlier user guides are a bit out of date.
I used a combination of the website from @Hani Dradi which really helped with the PostgreSQL installation and a second website as I was not sure what applications I should install with PostgreSQL using Stack Builder - the answer was only PostGIS.
Before trying to bypass, the issue you may look at you QGIS version. Some people encountered issues while using EPSG27700 but it seems to be fixed since QGIS 3.10.2 e.g https://github.com/qgis/QGIS/issues/33154#issuecomment-576350494 and another fix for another related issue has been done with QGIS 3.12.2 e.g https://github.com/qgis/QGIS/issues/35665
Install ESRI_Arcview.zip in C: Drive (this is just a zip of the C:\Esri folder from a previous install)
Install Common_files_ESRI in C:\Program Files (x86)\Common Files (again a copy of the previous files)
Install Fonts.zip in Fonts (esri_1.ttf to esri_9.ttf)
Create a HOME environment variable to point to a home folder
Install avenv.ave in the HOME ...