Well... Yes, *theoretically* it *should* be possible to do this...
HOWEVER....
You'll need to take the header of the most recent valid block, manually create a new header (
https://en.bitcoin.it/wiki/Block_hashing_algorithm), then you'll manually have to pick a nonce within this header and calculate the header's sha256d hash on paper... The odds of picking a nonce that leads to a sha256d hash under the current target is astronomically small. But let's say you find one: to finish it off, you'll have to find a way to broadcast your block to the other nodes (nope, afaik, there is no "website" where you can submit blocks, you'll have to find a way to broadcast it to other nodes manually).
To top this all off, you'll have to do this BEFORE the rest of the network finds a new block and broadcasts it... As soon as they do, the rest of the network will be using the new block's header to build their blocks on, and your block will be stale. So, you'll have to finish all these steps in an average time of 10 minutes... Maybe you're lucky and the rest of the network needs 15 minutes this time, but it might also be 2 or 3 minutes...
Now, i don't know how fast you are, but here's an article you could read:
http://www.righto.com/2014/09/mining-bitcoin-with-pencil-and-paper.htmlThis guy hashes 0.67 hashes/day, so if he managed to pick the right nonce, there'd be no way he was on time for broadcasting his block...
