The simple answer is almost certainly no. The complicated part is why -- the answer is based on evolutionary adaptation.

Mammals are members of a larger group of vertebrates, known as amniotes. This group includes reptiles, birds and mammals. (good link here).

There are also non-amniotic (anamniotic) vertebrates, for example fishes and amphibians.

Other extraembryonic membranes are also present,

The amniotic and the other extraembryonic membranes an evolutionary adaptation to birth on dry land.

These membrane surround the developing embryo -- they provide an water-rich environment, facilitate the exchange of gases (O₂ and CO₂), link to embryo to a source of nits source of nutrition (the yolk) and provide a place to store its wastes.

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As the embryo develops, its circulatory system is connected to the yolk through a system of blood vessels. Nutrients, stored in the yolk, are mobilized by the developing embryo.

In most cases, the shelled egg is a completely self-contained developmental system -- although it may have to be maintained at a particular temperature and protected from predators, it basically develops on its own.

There are in fact mammals, the monotremes, that lay eggs. When born, monotreme babies and extremely premature and develop substantially outside of the mother.

The other groups of mammals, marsupial and placental, have replaced the egg completely with an internal structure, the placenta.

In marsupials the placenta is a relatively simply structure that does not support the full development of the fetus -- which is 'born' premature (as in monotremes) and completes its development externally.

The placenta is very highly developed in the placental mammals, the most diverse group of mammals.

In many placental mammals, although not all, the new born organism is extremely well developed at birth.

The placenta acts as the link between mother and developing embryo -- it takes the place of the yolk. It is rich in blood vessels which transfer nutrients and remove wastes.

So, since the placenta is like like yolk, why can't we just re-engineer placental mammals to develop within a shelled, yolky egg?

The obvious reason is evolutionary. The earliest currently known placental mammal, Eomaia scansoria, lived ~125 million years ago. While the earliest known mammals, Eozostrondon and Megazostrodon lived ~210 million years ago.

This implies that placental and monotreme mammals diverged from a common lineage quite a while ago, and during the period of divergence many cellular and molecular adaptations have been incorporated into their developmental mechanism.

There are many interdependencies between developing embryo, placenta and mother that would be difficult to reproduce in a shelled egg.

Even having an embryo of one placental mammal develop in another placental mammal is non-trivial and only occurs between related species.