Thanks for this screenshot. When you try clicking any of the hair types, do they appear? I haven't tested this on Android 14 since I don't own an Android 14 so maybe that's a factor. Here's what you can try:

Download modelcustomization file from Gamebanana or my Patreon page: https://gamebanana.com/mods/610962
Place the file in "Android/Data/com.Nivium.iiMiiMaker/files/", overwriting the one that's already there (If one is there) then restart iiMii Maker. See if that makes a difference. Also I apologize for getting back to you so late. I have been checking Itch.io everyday and have gotten no notification. I only saw it when I manually checked the comments of posts.

Hey! Good news. I believe I know what the problem is. If you're having this same issue, two files will probably be missing from your folder.
You CAN fix it yourself right now if you want but I'm hard at work making an update for it either way.

Navigate to Android/Data/com.Nivium.iiMiiMaker/files
Place 2 files there:

DefaultM.iimii
DefaultF.iimii

You can grab any of the .iimii files in iiMii folder and copy-paste it there and rename it. These are the default Miis (Which are planned to be customizable in the future) which it seems the game didn't create for you on startup, as it should have. (If you don't have any .iimii files, you can get some from Reddit in the /iimii subreddit posted by SirenXY. I know this is a bit inconvenient if you don't use that platform. Otherwise just wait a bit more for the update that hopefully fixes your issues.)

EDIT: The update is out. Please try it out!
If you still get the same error, click and hold the app icon, go to App Info (Settings of the app) and ensure you allow Permissions (Photos and videos). This permission allows iiMii Maker to detect iimii files. (The default ones, specifically)