The "Go to first unread post" button exists, it just doesn't show up if you have already viewed all of the current posts on a thread.
If you click on a thread that you haven't seen all of the replies to, the button will appear at the top and also at the bottom of the page I believe.
If you look at the left of all of the forum sections, you will see that the chat bubble icons are shaded differently depending on when threads are read vs. unread.
I believe that the icon becomes darker when there is an unread thread or post. If the colors are too hard to differentiate between, I can fix that.
Edit: Here is a screenshot of what the button looks like;
View attachment 2
I'll be changing the text over it to white though, to make it more visible. The same goes for the page numbers.
Edit #2: I have changed the color on the page numbers and the "Go to first unread post" button to white so that it is easier to see