Looking at this bathroom sink from below a round area is visible in the middle where the material is thinner. Is there a safe way to drill a middle hole there (to install the faucet recommended at https://diy.stackexchange.com/a/18330/7480)?
I would not recommend treating the area in the center rear of the sink as a "knock out". Trying to remove that portion of the sink with a hammer is foolhardy at best and could lead to splintered and cracked procelain on the top side of your sink.
You would be far better off to apply a hole saw made for this type application. Here is an example of a diamond grit hole saw that may be suitable:
Link to tool on Amazon:
Hole saws of this type are often used with a 0.25 inch diameter drill bit acting as a centering agent to keep the hole saw in its cutting track. It is often a good idea to pre-drill the guide hole for this before deploying the hole saw. Look for a diamond dust drill bit for drilling this hole.
Use of the hole saw will likely require the adding of water into the cut area during the cut process to keep down the heat buildup on the hole saw.
If it was my project - I would drill the guide hole from under the sink first in order to get it centered properly and then come back and drill out the necessary larger diameter hole with the hole saw from the top side.
Last Comment - Before investing a whole lot of money in tools for a one-shot project you owe it to yourself to investigate the cost of a complete sink replacement that has the appropriate hole configuration to meet your needs. You may find that a retailer may offer a good deal on pricing if you purchase a sink and faucet at the same time.
The thinner part is a knockout. Give it a firm tap in the center and it should break out cleanly.
EDIT: Four upvotes to Five downvotes... Interesting ratio. I'm curious of the downvoters: What do you think that thin circle, in the center of the area where a faucet would go, with a formed center tapping point... is?