1 TB per month of data is literally nothing. A kid could rent a VPS for an hour and drain all that. What do you do after that? AWS is not going to stop your bill going up is it?
I don't care about any of those fancy serverless services. I am just talking about the cheapest CDN.
Ah, for cheapest CDN, maybe you're right. I think BlazingCDN can also be cheap, but CLoudFlare might be the best deal. OP didn't really say there wasn't any cheaper alternative, just said "no real good alternatives".