@Simon, it looks like you have the command line tools installed. In Finder, find the SDK you installed and search for a file called "android". Mine is in <SDK folder>/tools/android
Double click "android" to let terminal launch the Java app. You should see the SDK manager and a list of all files available with those that are installed tagged. Take a screenshot of the window and post it here. It may be that your existing SDK just needs to be updated. See if any of the above files have updates available and download those.
If you don't see any of that then it may be true your SDK isn't valid. Delete your SDK, or move and rename it. Go here:
https://developer.android.com/studio/. Scroll to the bottom of the page and download the Mac command line tools (zip file.) Unzip and install. Then open the "android" file and launch the SDK Manager.
You need the Android SDK Tools, Android SDK Platform-tools, and Android SDK Build-tools. Build-tools should be version 28.0.1 or higher (I'm still using 28.0.1 and it works.)
You also need the Android 4.0.3 package, and also, optionally, any other packages you might want to emulate. I have Android 6.0 installed as well as several other lesser versions. When installing the Android version packages you don't need all the files, usually only the SDK Platform file for each version is enough.