Something you can do always on a Linux system as a user is to run the AppImage with LD_LIBRARY_PATH=".:$LD_LIBRARY_PATH" ./Your*.AppImage and, before that,

Something you can do always on a Linux system as a user is to run the AppImage with LD_LIBRARY_PATH=".:$LD_LIBRARY_PATH" ./Your*.AppImage and, before that, put all the missing dynamic libraries in the same path. That task might however be nontrivial due to (hiearchical/nested) dependencies (try "ldd *.so" to inspect it) of the so files itself. That's one of the reasons why we have package managers at the first place...