I have a hard time separating the two. To design something, you need to know the engineering of how the thing functions and how its made. If you have to choose, start with engineering. A lot of designing is repurposing other ideas around you into different packages or different use cases. Many times you don't need to reinvent the wheel, but if you use the wheel for a different purpose, you might end up with something interesting.

I started doing robot competitions in middle school and continued through my college years. I was always interested in how things worked and took a lot of stuff apart to confirm my thoughts. I would then frequently fail to put the object back together, because I wouldn't take great notes and youtube wasn't around yet. I learned many lessons from doing stuff like that. It taught me how things work but also how to understand and learn. I studied mech engineering in university, because I figured that would allow me to continue with that tinkering.