Idk exactly how to answer or have one really but don’t give up keep reading…
You have several options some of which I have no clue how to do but am throwing around in my brain maybe create a popup…depending if you have content on your main site this should work creating a popup and having them choose their option then navigating them to the sub domain
The Pop up plug in I use is called WordPress Pop up its pretty good I use it for all my sites I have and use it to display buttons and so forth so you should be able to use it to your advantage…
Another way to do it is make your own using HTML since (I am assuming) you’re using you are able to use Java and so forth with more freedom. With that said here are some links to help create those menus your self just note when you’re adding these instead of the normal writing (visual) switch to the text tab and type your html in. I will mention one of them has a Css option on doing something if the sort I’m unsure on that
I am unsure if you know how easy it is to use html I am a very low level in html yet I understand it I am still uncertain in some areas but…any ways I hope you get your problem/solution/objective completed!
Sorry about so many links but sometimes they don’t always work the solutions so I have many to try!