I slept on the floor for a couple years on a fold out foam pad, basically 3 cushions sewn together similar to this but without the memory foam layer. Foam was about 4 inches thick and I didn't bottom out at all, was around 150lbs at the time. Slept very comfortably.

If you're really tight on space, take a look at sleeping pads for camping. There are some roll ups that are made of pretty advanced materials you could potentially sleep on without problems.

Frankly, though, if there might be cockroaches or pets roaming around, I might instead sacrifice some space to use a cot frame with some DIY roll out slats under a pad. Edit: you can buy roll up slats.