How can someone from a different field like engineering transition to product management?
I'm a fan of pairing. Often times Engineering works so closely with product, it is easy enough to sit more closely with your product partner and work through problems together. Ask questions and learn while on the job. If and when you get comfortable enough, start to volunteer to take on different tasks. I've worked with engineers who pair with me in writing requirements, buidling out tickets, reviewing designs, conducting user research. With this, you can now speak to first hand experiences and learnings within your existing company or any new ones you may be looking to move into.
Fairly easily potentially, compared to transitioning from other less-related fields. Product Management is as much art as it is discipline or science. Leveraging technical expertise related to the same or adjacent PM area helps. Some job descriptions will even require engineering experience or area of study. One major pitfall to avoid however, is remaining in "engineering mode" as a PM. As PMs, our focus should be on the WHAT, WHO, and the WHY, whereas Eng/Data Science's focus is more on the HOW. While some may disagree, for me all these still fall in the category of Hard skills for PMs. As an engineer transitioning to PM you would need to potentially learn more about setting product vision and strategy, go-to-market strategy, user requirements gathering, writing product requirements docs, and prioritization. You would also need to flex a lot more of you soft skills as a PM: communicating in writting and verbally, synthesizing info, influencing, managing stakehorders, driving collaboration and execution, prioritizing, negotiating, inspiring, etc.
This can seem overwhelming. So "How do you eat an elephant? One bite at a time." Ideally, you have the technical experience in the same business domain, and can read up plenty on the discipline of Product Management. You've likely even experienced all this on the receiving end as an engineer. The rest is the art and the soft skills which will come with self-awareness, observation of your own and other's interactions, practice, and even formal training. While you may not be crafting product strategy on day 1, getting as much exposure to frameworks for strategy, and even just listening to others make strategic decisions and trade offs will help you start applying similar frameworks yourself.