As mentioned above, 4G and 5G networks are intended for phone to phone communication (voice or texting), and do not have public access points.
But I do see what you wish for.
Imagine you are calling another device to speak on the phone. While the line is open you can communicate with the other party at a respectable fast rate.
Now, how can you use that open line to communicate data for your game. Remember the line needs to be kept open, otherwise your latency will be affected.
Therefore texting is not practical.
If you have a free plan for a region, then open lines may be practical, for example I have a free plan for within Canada cell phone use.
Then if you could encode digits to sounds and decode then back, you could have what you want. For example DTMF.
This is a lot of ifs, and DTMF (touch tones) are not very reliable.
Food for thought.