That's exactly what I was thinking. My old coop below was on cement blocks, slightly above ground level. (The hardware cloth extended another foot underground)
This pic was before I had finished the interior door or nestboxes - not that the chicken's cared!
But the ground in the run...
That's why I was wondering if you could take any bricks out. If you have bare soil, you can do the deep litter method in your run and only clean it once or twice a year.
On a hard surface you have to clean more often since there are no soil organisms to help break down the waste. So yes...
X2 what OFW said. Any way you could remove a section of brick in the run so the chickens could dig in the soil? If not, I'd go with the sand and straw. Just know you'll need to clean it out a lot, so don't get too many chickens for your space.
When I had a small coop like that I just covered the bottom of the coop in PDZ and sand. (Painted the wood floor with a fence/deck sealer first.
Scooped it out every other day with a long handed kitty litter scoop and put the waste in the compost.
Are you going to let your birds out in the...