I'm not sure what you mean by "going up to the screen"?
There are many ways to send a text. The quickest would probably be to have a shortcut to text the person you want to text on your desktop. To do this, long press a blank area on your desktop, select Shortcuts, Direct Message, select the contact/number. From now on when you press that shortcut it'll go straight to the screen where you type your message.
Of course, that only works for one person, so maybe just a shortcut to your Messaging app or Contacts app might be better?
You can also make keyboard shortcuts to any app, but I don't know if that only works on phones that have physical keyboards.