Personally, I wouldn't recommend cross-compilation, since it can be a lot of pain to get working properly and running Windows in a VM or on a different machine has also other benefits.
If you do want to keep cross-compiling, you'll need to get cmake, the SFML
source code, configure CMake to use your MinGW compiler and follow the
CMake tutorial on build SFML as a library with your current compiler.
Or did you actually already do that? Your post always left me a bit inconclusive about this.
I realized that it is more convenient to build on Windows, but I want to try because I'm the beginner.
Nothing is stopping you from trying stuff, but it's usually better to start on an easy level as a beginner, until you're more familiar with a topic and can understand why something is or isn't working on your own.
You also don't pick the hardest possible game mode and then complain and give up because you can't finish the first level, since you don't understand the required mechanics.