After not being able to find a link explicitly answering your question I am giving you my understanding of it - and I may not be entirely right!
The first thing is that the radiation that is measured was actually created about 400,000 years after the big bang, before that the universe was too dense for light and radiation to exist for any length of time. We cannot 'see' any universe activity from before this time although there are thoughts that measuring gravity waves from this time will allow us to do this in the (distant) future.
The radiation that is measured didn't actually travel from a single point TO the Earth, we are not special in that respect! Rather it comes to us (and everything else in the universe) from all directions.
Think of it as we are detecting 'light speed' signals that are hitting us now that were generated from an event that happened 13.7 billion years ago. The actual signals that we are measuring have indeed travelled 13.7 billion light years in distance to get to us but that is just because we are measuring NOW, if we were measuring 10 billion years ago, the signals would have only travelled 3.7 billion light years to get to us but this has nothing to do with the actual 'size' of the universe either back then or now.
Be interested to see what people think of my understanding of it all! Interesting question...