Building OpenSSL has gotten really easy these days and a lot of arcane things that I had to do to build version 1.1.x with cygwin and Visual Studio 2017 or version 1.0.2x are now a thing of the past. However, one thing I first had to do to build version  3.1.4 for android was updating cygwin to a more recent version than in the past, because  the old version I used before has some trouble using the configure script from version 3.1.x, most probably because the version of perl was too old. So I installed the most  current x64 version of cygwin at the time of writing  (3.4.9) into c:\cygwin64 and besides from a default install I added the following components  to the install:

automake, patch, perl, dos2unix, make, makedepend

You can download the full list of components in my cygwin installation here.

Since the build scripts for OpenSSL on Linux make heavy use of symbolic links for header files, you should also turn on "Developer Mode" on your build and development host (which should be Windows 10 10.0.15063 or later), otherwise the build scripts cannot be executed successfully by a standard user. From Windows 10 10.0.15063 on, symbolic links can be created on Windows machines without administrative permissions if the box is running in "Developer Mode".

In the following I assume that cygwin is installed into c:\cygwin64. In case your installation directory is different, set an environment variable named "CYGWIN_PATH" that points to your installation directory of cygwin prior to invocation of my build scripts, or edit the file named createcfg.bat among the script files in the zip for this article and set the value of "INTERNAL_CYGWIN_PATH" in this file to your cygwin installation path.

I further assume that the NDK that comes with Visual Studio 2022 is installed in c:\Microsoft\AndroidNDK\android-ndk-r23c. In case it is someplace else, set an environment variable named "OPENSSL_ANDROID_NDK_ROOT" that points to your NDK installation prior to invocation of my build scripts, or edit the file named createcfg.bat among the script files in the zip for this article and set the value of "INTERNAL_OPENSSL_ANDROID_NDK_ROOT" in this file to your NDK installation path.

In  order to build version 3.1.4 of OpenSSL for Android first download this zip file containing my scripts onto your Windows box with Visual Studio 2022 and the native Android build tools installed. Unpack the file into a directory and a subdirectory named "androidopenssl3.1.x" will be created. Open a command prompt and navigate into this directory. Now download version 3.1.4 of OpenSSL here (in case this link doesn't work, try this one which should point to the archive of old builds) and copy it into that directory as well.

After all that, run the build.bat batch file within the command prompt and sit back. On my Ryzen 5 5600X it takes something like 25 minutes to build the whole shebang. You will find 4 subdirectories (arm, arm64, x86 and x86_64) for the 4 supported processor architectures that each contain a directory with the name of the openssl file name (without the extension tar.gz, so in case of version 3.1.4 of OpenSSL this directory name is "openssl-3.1.4"). Within that directory you will find libssl.a and libcrypto.a built for the corresponding processor architecture.

In case you would want to build dynamic libraries as well, edit the file buildplatform.sh and remove "-no-shared" from the configure options.

And finally: If you want to build a newer version of OpenSSL than 3.1.4, download its tarball into the directory where you unpacked the build scripts and change the value of "OPENSSL_VERSION" in createcfg.bat from "openssl-3.1.4" to the name of your tarball (but without the extension ".tar.gz"). Do the same for "ANDROID_API" (which is set to the value 23 in my scripts) if you want to target a different Android API version than 23.

 The license for these shell scripts of mine is the same as for OpenSSL, so nothing should change for you.