I had that situation a few years ago camping at a local state park.
It rained. A lot. Reports were that the nearby town received ~5" of rain - and back in Austin the east side received ~10"+ resulting in flooding out of many homes in Onion Creek.
The ground around my tent was relatively level, but this resulted in ~1/2" of water everywhere. I could feel the water from below my tent (REI Quarterdome) but it really hadn't leaked into the tent much at all. I was one my thermarest which kept me up off things. The worst of the storm and heaviest rain was coming through ~4am - so I waited things out on my island until closer to daylight. At that point, I quickly brought everything out of the tent to nearby covered picnic table. From that point, I could pack everything in and cycle to town for breakfast inside. After that the most intense rains were already past, so except for detours to avoid four places where water was running well over the roads - make my way back to Austin.