This is not a bad question, but the premise is all wrong.

nile, the Indus and between the Tigris and the Euphrates?

I am not sure where you are getting the idea that these are tiny oases dwarfed by your other examples. All of the early civilizational cradles you listed are large, highly fertile rivers with massive valleys and floodplains.

Take the Nile for example, which is ten times the length of the Po. It has one of the largest river deltas in the world. In terms of geographic size, the Nile Delta (about 100 x 150 sq miles) is smaller than the Po Valley, but the difference comes down to how much of each valley is well suited to agriculture. The Nile Delta is flatter and has a higher proportion of highly arable land, so it's better suited to early human settlement.

The majority of ancient Egypt's population lived either along the Nile, or in the Nile Delta rather than in less habitable regions like the Red Desert. And this trend never really ended. In modern Egypt, the population density of most regions along the Nile is in the low thousands per square mile. Only once more sparsely inhabited regions are included does the national average population density decrease to about 250. Similar trends can be observed in other African countries along the Nile, which have their populations concentrated around the river.

There are other features of the Nile which make it more well suited to agriculture. The Nile floods annually, and washes rich silt onto its banks which replenishes the soil. Even today, it has incredibly thick topsoil. This made farming much easier in Egypt than it was in Europe. Not only did soil not need to be tilled as often, but Egyptian farmers were able to get better yields.

It is difficult to estimate crop yields in prehistoric Egypt and Italy, but we can compare crop yields in Roman era Egypt and Italy. Farmers in Italy might have expected a seed yield of 10:1 if they had a decent harvest on very good land. This was much better than the 5:1 that Italian farmers yielded on average, and the 3:1 seed yield required for subsistence farming. Farmers in Egypt at the same time would have expected yields between 16:1 and 22:1. In fact, they would have had to grow that much in order to afford the exorbitant grain taxes levied by Rome. The difference in agricultural output speaks for itself.

The difference in food production had a major impact on population density. Late Period Egypt had a population of at least 4 million, with a population density of at minimum 300 people per square mile. Higher population estimates range are up to 7.5 million. While some of these people lived in metropoles like Memphis or Alexandria, most lived in the tens of thousands of villages throughout Egypt. It would not have been possible to travel more than a couple of miles from one of these villages before reaching another. Roman Italy never approached the population size or density of Egypt, although the city of Rome dwarfed the Egyptian capital of Alexandria.

Even under conservative estimates, the population density of 1st Century BCE Egypt was equal to or greater than modern day France. We are not even comparing it to premodern France, which obviously had a much smaller population.

That addresses the agricultural fertility aspect of your question, the reasons why complex civilizations developed in certain regions at certain times are much more complex. Agriculture was definitely one piece of the puzzle, but it is not the whole answer.