Based on my experiences with programming, I imagine part of being able to think this way is also having experience building things physically. The fact that I can think about connecting pieces of backend infrastructure, or bits of reusable code, or a wiring up a handy library to solve a problem is from experience solving problems with the tools at hand.
Probably the best way to get started with this mindset in any problem domain is to just start making things, getting a feel for the capabilities of tools, the strengths of various materials.
In other words, the attitude adjustment is just one part of being able to solve problems this way - you've got to be very comfortable with your tools and materials, or have little to lose so you can experiment safely.