Is it possible to pre-compile a library into a for example MyCoreLibrary.o and in Arduino IDE just include the MyCoreLibrary.h files?
There is a precompiled feature that was just added in Arduino IDE 1.8.6 and newer. To enable it, you need to set the precompiled field in the library's library.properties file to true. You can find more information here:
Later versions of the IDE have the ability to use pre-compiled libraries. This means that the end user only gets the compiled version of your library (a .a file) rather than the source code.
Modify your library.properties file to include dot_a_linkage=true. If you don't have a library.properties file you need to make sure you create your library in 1.5.x format.
Then compile your library in the normal way. This will result in a .a file somewhere in the build tree which gets linked with your sketch. You need to grab that .a file.
Next make a new copy of your library that has just the header file (needed for compilation) and the .a file (needed for linking). No .cpp files.
Now you in the new library.properties file you add precompiled=true.
As long as you lay out the files right it should now compile using the precompiled .a file.
You can read more about the library.properties contents here.