Is it possible to somehow send a new block to the btc network without using ports?
One of those questions where the answer is in the question...
If you are talking about the bitcoin network you mean there are machines connected on a network, and they need a protocol and a port to create that network.
Now, if we think deep in the question, the right answer is: It would be possible if only you are in the network and you mined that block. A good example is the first block ever mined, it was only one computer in the network, think about it