Yes, a UX designer can become a product designer, and it's one of the more natural moves you can make in this field. Most people who've worked in both roles will tell you the line between them was always blurry. The two aren't separate tracks so much as different points on the same path.

UX designers already know user research, problem framing, wireframing, prototyping, and usability testing. Product designers need all of that too. What changes is the scope. Product designers own more of the surface area, from visual polish to business trade-offs to shipping decisions.

A few things tend to matter most when making this move:

At startups, this transition often happens without anyone planning it. You join as a UX designer and within a few months you're making UI decisions, sitting in on product strategy meetings, and filing bug reports. At larger companies, you usually have to push for it. Ask for broader responsibilities. Volunteer for visual design work. Get involved in roadmap discussions before anyone invites you.

Your portfolio matters too. Case studies that show the full arc, from research through final UI to measurable outcomes, will do more for you than ones that stop at wireframes.

The skills are mostly already there. It's really about expanding how you think about the problem and what you take ownership of.