The journal Science had an interesting article about the correlation between the climate of ancient Egypt and the archeological record.

This is a map of Egypt from the article, showing the different rainfall/vegetation zones over a period of about 5,000 years. As you can see, prior to around 9,000 BC, Egypt was mostly desert, much the same as today. Maybe even a bit drier than today, with the Sahara marginally larger.

Between about 8,500 BC to 7,000 BC, the climate got rainier. The monsoon shifted northward from the area it usually covers, i.e., central Africa. This is the neolithic subpluvial you mentioned. As you can see in the map, the wettest zone is to the south over the Sudan, but there were extensive grasslands in Egypt as well. This wet period lasted until about 5,300 BC, when it started getting drier again. This drying was fairly gradual until about 4,000 years ago, when it suddenly escalated and became bone dry over less than a hundred years.

The red dots on the maps are ancient settlements as seen in the archeological record. In the early desert phase, the population is clustered on the banks of the Nile near the Sudan border. But in the wet phase, population centers spread out over most of Egypt. These northern regions of Egypt were mostly grassland. In the earliest phase, the people were foragers, but pastoralism was becoming common. Agriculture arrived (relatively) late - just as the climate started to dry, around 7,000 years ago. The oldest evidence of agriculture in Egypt is from the Faiyum region, which is geographically a depression, and probably held a lake at the time. The lake is now an oasis with the encroaching desert, but people still farm there to this day.

The last panel on the map shows the period 5,300 BC to 3,500 BC and we can see that population centers have moved back to the Nile, except for a very few scattered oases in the desert.

So there were a number of environmental pressures on the people at this time. First, the population had grown significantly during the wet period, and as the climate gradually dried, these people were forced to move closer to the Nile. So population density in the Nile region increased, and this smaller region had to support a large population. The bulk of food calories now came from farming, although pastoralism was also prevalent a bit farther from the Nile.

As the climate continued to dry out, irrigating the farms became a problem. The ancient Egyptians developed a network of canals for this purpose, which required the coordinated labor of a large work force. This may well have been the beginning of political organization. As early as the "Scorpion King" (3,100 BC) we have artifacts such as this mace head showing the King ceremoniously opening the dikes in a grid-like network of canals. Maintenance and expansion of the water supply for farming was obviously an important role of whatever political authority first appeared in Egypt.

Interestingly, farming and irrigation appear first in upper Egypt (the southern part of the Nile), while farming appeared first in lower Egypt. Perhaps this was because the Nile delta had a Mediterranean type climate which was wetter, so the need for irrigation was felt later there than in the south. The Scorpion King wears the white crown of upper Egypt.

Here's another figure from Science showing the correlation of archeological sites with climate. The y-axis is latitude, with north up. The x-axis is time. The color coding shows green for wet climate, brown for desert. As you can see, desertification appears as early as 3,800 BC in the north, and as ;ate as 1,000 BC in the far south. There are many stone monuments found even today (especially in the south) surrounded by desert. They were originally built when the landscape was lush and green, but were later abandoned to encroaching desert. You can kind of follow the progress of desertification from them.