How to sleep on a folding sofa bed more comfortably?

I would get a good 3" thick piece of high density c shion foam (3" thick x 3 "wide and as long as the hinged area.) Wedge it in the crease to pad the hinged area as you flatten the couch. Thin proceed with the topper for added comfort and breathability.

Ask a local upholestry shop if they have any cushion remnants.

Oh, I just thought of another idea...When folks join two twin mattresses together to create a king size bed, the crease can be bothersome. There is a " T" strip available at mattress stores to fill that gap. Maybe that would be a good solution for you, perhaps.

How to Make a Pull Out Sleeper Couch More Comfortable

Add a Mattress Topper. The easiest way to improve the comfort of a sleeper sofa is to add a mattress topper. ...

Buy a New Mattress. Another way to improve the comfort of a pull out couch is to buy a new mattress. ...

Fill in Gaps With Pillows. ...

Sleep on Quality Bedding. ...

Keep the Mattress Clean. ...

Sleep on a Duvet.

That is a pretty slim couch, more a futon. There is only so much comfort you can gleam from it. 

I would have gotten a thicker foam topper. 

Yes you can out a partial board in there to help.

But how often are you going to be using this bed? Do you have to open it up every night and close it every morning? 

We have a futon on the front porch like that.  The frame poked through the mattress and you could feel it.  So my husband went to Home Depot and bought a "high density particle board" that is not very thick, had them cut it to the dimensions.  Painted it and put it between the frame and the mattress.  It is very comfortable now.

My advice would be to return it as unfit for purpose. If it is sold as a sofa bed you should be able to sleep on it, providing it is correctly assembled.