Like other skills it can absolutely be cultivated.
Even if one doesn't "naturally" care about others, it's also true that even from a totally selfish perspective it still kind of pays dividends to be a good person, be concerned with the welfare of the people around you, and build interpersonal connections.
There's limits to that, for sure. There are a number of biological bases for empathy. And being biological, it stands to reason that different people will have different capacities. But, it also certainly feels like a skill.
Here's another angle. A lot of people, perhaps maybe a lot of engineer types, struggle with empathy because the needs and wants of others just feel like a confusing sea of infinite possibilities. But here's a trick. At any given moment, any given human being is probably just trying to fill one of the needs on Maslow's Hierarchy of Needs.