TextMesh Pro Trying to create 'search' UI

I want the user to be able to start typing in an input field and an autocomplete list of possible options appear below for them to select. I'm overlaying an input field on top of a drop down. Every time the user changes the input field the drop down is populated with the relevant options and the user can select one if they want to, or continue typing to update the list some more.

The problem comes when I force the drop down to display its list of options by using Show(). This forces the input field to lose focus and the drop down to gain focus, meaning the player has to click the input field after typing each character to regain focus.

Is there a way to make the drop down show its list of options without being in focus? Or am I better off just making my own drop down list system?