Unfortunately this can not be done without databases a lot of code (At this time) . Currently you can only access the user ID, their Email, and their roles.
if the email works for your needs that can be achieved with the following
//Page Code
import wixUsers from 'wix-users';
$w.onReady(function () {
wixUsers.currentUser.getEmail() .then( (email) => { $w('#ID_of_the_text_box).text = email } );
});
For achieving this with usernames I am currently using a system where users set a screen name and other info when they first create their account and it saves that to a database that can then be called from with a query. This however requires extensive code.