I push the "create character" button and nothing happens. I validated the game via the Launchpad https://pasteboard.co/754gwc48mSiJ.jpg
Try going into full screen mode but if that works then you will need to return to windowed after Full-screen vs. windowed mode = ALT + Enter and toggle it again to go back
In your screenshot I can see that the EQ window might not be the active one. It needs to be active to let clicks work. You can activate it by clicking on the white window bar on the top or by the task bar.