Create breakout for small FPGA in BGA package
Since the comments are going too far I am giving my opinion here.

You should search for a commercial evaluation board with a device similar to your target, possibly with the HDMI connector already soldered. There is a ton of reasons behind my opinion, I am giving what comes to me from the top of my mind.


This seem a one time project - no production, no board selling - designing a whole board just for that is a waste of time.
You don't seem to have the know-how: an FPGA is a great, fast beast: it would need a lot of decoupling capacitors, you should put extra care in traces impedances, especially the HDMI ones, you should take care of a whole lot of things that you would encounter during the PCB design phase and possibly after the first prototype.
You don't seem to have the appropriate hardware: soldering that package without a reflow oven is impossible, soldering the other components might be feasible but... Have you ever soldered even 3216 parts? (I love the SI).
You don't really want to deal with all the other things that an FPGA needs to run properly: what about the clock? What about the programmer? What about power? These guys can draw quite a bit of current.
I am pretty sure you can't do a multi layer PCB on your own... Nobody probably can anyway.


That said, your best option is to just buy an EVAL board and stick with it.