I'm currently checking the web site www.alcatrazcruises.com to book an Alcatraz tour 2 weeks from now but they are fully booked. Is that web site the only way to book a tour of the island? Will it be possible to show up at the pier and getting on a ferry there to the island?
The National Park Service has an arrangement where only a single company is granted an exclusive franchise to travel to or take guests to Alcatraz. Therefore, if you want to go to Alcatraz, there is only one company you can travel with, and private boats are forbidden.
There are a few other websites when you search, but I can't vouch for any of them. What you could do to confirm is to call Alcatraz Cruises Box office: +1 415 981-7625, or email them (firstname.lastname@example.org). However, even when I was in San Francisco last year, tickets were sold out online and it wasn't possible to buy them in person on the day. However, that was Fleet Week, so your mileage may vary on a different week. I'd drop them a line and see what your options are.