I am not from Laminar Research just a flight simmer from downunder.
What do you mean by ".......But I don't see anywhere to install it?....." ?
I have a first issue disk version of X-Plane 11 (ie 11.00) and installed it on my laptop to ascertain if I would experience your problem.
I ran the installer and it automatically asked if I had a digital download version or a disk version. Immediately after I inserted disc 1 I received the message you initially read which was there was a new version available asking if I wanted to update. I refused to update until my version 11.00 was fully installed as I was trying to emulate your situation ie no updates performed during initial installation.
After shutting down and then restarting, I was again confronted immediately with an update notice. At the bottom of the page there was a tab asking if I wanted to update. I chose to do so. These prompts continued until X-Plane had updated to version 11.35
The installation I have just completed is on my laptop and not on my flight sim PC. I know that when I progressively updated on my FS PC to version 11.26 I had no problems as I could clearly see the continued blue tabbed question at the bottom of the screen, right hand side, asking if I wished to continue.
An additional question I have for you is, what screen resolution are you using? If it is not 1920 x 1080 (best visual performance for X-Plane) but at some lesser density then you will have to scroll down to see the full page being displayed. If your installation is on a laptop you may still have the need to scroll down the page.
If your screen is not at the recommended resolution then I suggest making the change to ascertain if your problem is solved.