How does craving cause self-identity or self-habit?

What one craves that one also clings to.

A newborn baby doesn't have self-identity ideation but it is not without an inclination to it's development due to past circumstances.

Does self-identity or self-habit arise out of a collection of likes and dislikes?

The adherence to the doctrine of self and ideation based on the doctrine of self are not something that not having been arises.

A baby is then without an adherence to the doctrine of self but the body is the result of past adherence coming into play.

It is the delusion which is without a beginning. The intellect goes through stages of devopment and it's default undeveloped course of understanding & thinking is in terms of the doctrine of self, that doctrine of self & adherence are evidence of delusion and what sustains existence.

It is with the clinging aggregates that the world becomes solid. One common word that describes this is reification. Andrei Volkov gives some details about that in his answer. This is true even when people have lost arms and legs. They are convinced that they can still feel that arm or leg. Through craving their aggregates cannot let go of the concept of body-form.

This same thing happens when we die. When we lose our body the idea of who we are experiences trauma. This trauma is the self-identity or denial of emptiness. As a response to that trauma it re-conceptualizes a new body-form just like the person who loses their arm. Through craving, the concept of arm continues; through craving the concept of body-form continues. The karmas of the previous body-form appear as sankhara-potential in the new body-form. It is a potential because it needs to develop an understanding of the world it now finds itself within so that its sankara contours can be played-out. Babies are abundant with sankara-potential, you can sense it in them, but due to their innocence they are not able to fully display those sankharas. Their actions, thoughts and speech are barely operational. Therefore, sankharas are the etchings, contours or indentations truncated into an individualized claimant and the claimant represents prior craving through here-and-now ignorance, but of course, we cannot see that bigger picture!.

The repetitious nature of it all makes it difficult to see the details, and so I don't think your question can be answered with any degree of accuracy. At best, only a theoretical understanding might quench your curiosity, but only temporarily. It's almost as if you're asking which came first, self-identity or craving. Maybe this section of DN27 might help with understanding self-identity, craving and especially reification leading to coarse and dense forms.

'There comes a time, Vasettha, when, sooner or later after a long period, this world contracts. At a time of contraction, beings are mostly born in the Abhassara Brahma world. And there they dwell, mind-made, feeding on delight, self-luminous, moving through the air, glorious — and they stay like that for a very long time. But sooner or later, after a very long period, this world begins to expand again. At a time of expansion, the beings from the Abhassara Brahma world, having passed away from there, are mostly reborn in this world. Here they dwell, mind-made, feeding on delight, self-luminous, moving through the air, glorious--and they stay like that for a very long time.

'At that period, Vasettha, there was just one mass of water, and all was darkness, blinding darkness. Neither moon nor sun appeared, no constellations or stars appeared, night and day were not distinguished, nor months and fortnights, no years or seasons, and no male and female, beings being reckoned just as beings. And sooner or later, after a very long period of time, savoury earth spread itself over the waters where those beings were. It looked just like the skin that forms itself over hot milk as it cools. It was endowed with colour, smell and taste. It was the colour of fine ghee or butter, and it was very sweet, like pure wild honey.

'Then some being of a greedy nature said: "I say, what can this be?" and tasted the savoury earth on its finger. In so doing, it became taken with the flavour, and craving arose in it. Then other beings, taking their cue from that one, also tasted the stuff with their fingers. They, too, were taken with the flavour, and craving arose in them. So they set to with their hands, breaking off pieces of the stuff in order to eat it. And the result of this was that their self-luminance disappeared. And as a result of the disappearance of their self-luminance, the moon and the sun appeared, night and day were distinguished, months and fortnights appeared, and the year and its seasons. To that extent the world re-evolved.

'And those beings continued for a very long time feasting on this savoury earth, feeding on it and being nourished by it. And as they did so, their bodies became coarser, and a difference in looks developed among them. Some beings became good-looking, others ugly. And the good-looking ones despised the others, saying: "We are better-looking, than they are." And because they became arrogant and conceited about their looks, the savoury earth disappeared. At this they came together and lamented, crying: "Oh that flavour! Oh that flavour!" And so nowadays when people say: "Oh that flavour!" when they get something nice, they are repeating an ancient saying without realising it.

Agganna Sutta