I can’t think of a project like that that people said couldn't be done, its usually just people saying “we cant do it at this time unless we get more time or reprioritize something else.”
We had a bunch of UXR that showed that people liked iPhones because of the fancy snappy animations, and our execs really wanted to bring that to Google's webapps. At the time, there was this big perception that mobile web sites were slow and clunky and you absolutely had to go native app to get smooth 60fps transitions. I did some profiling with the Chrome profiler and found that the bulk of time was spent in layout & reflow, and that one single reflow would blow your entire frame budget and then some for 60fps on mobile. So then I went to the Chrome GPU team and got a quick tutorial about exactly which operations were handled on the GPU (basically just transform and WebGL, at the time), and put together a visual language that basically involved rendering portions of the webpage to GPU textures and manipulating them only with 2D transforms, which could be GPU-accelerated. The work later formed the foundation for how Material Design was implemented in Search.
As a side note, I learned a lot about how browsers work under the hood with that project, and one of the things I learned is that the entire premise that React was sold with was false! At the time, the big selling point with React is that "DOM manipulation is slow, so we create a virtual DOM that's fast and then diff the changes to the virtual DOM so we make only the minimal set of DOM changes we need." Except that every major browser by 2013 used a dirty-bit system for DOM manipulation, so changes to the DOM are actually quite fast (roughly the speed of a couple pointer manipulations in C) as long as you don't trigger reflow. And you can trigger reflow with any one of about 2 dozen method calls, as well as automatically when you return from a Javascript script fragment, so basically every Angular and JQuery website was triggering multiple reflows per event. React was fast because it was declarative and didn't let you execute user code until it was done batching up all DOM manipulations, it wasn't fast because of the virtual DOM. And I believe there have been re-implementations of the React API that do away with the virtual DOM and they are equally fast (oftentimes even faster, since they're simpler and don't need the DOM diffing), but at this point React is popular because it's popular and everyone knows the API, not because of any purported performance benefits.
This is all for IC engineering. I actually prefer to think of the ladder in organizational terms which also encompass management, but the sub-thread here is specifically interested in what it takes to be an L6+ IC.
Management thought of me specifically because I'd built a reputation as someone who could tackle difficult projects, particularly those surrounding browser UI. I'd worked on the last 3 visual redesigns of Google Search (as the first engineer of the 2010 one, a consultant for the 2011 one, and the tech lead of the 2013 one), plus I started the Authorship project within Search, plus I'd done a bunch of little visual easter eggs like the [let it snow] holiday one (also a project that many people thought was impossible because it was started after the last binary push of the year). Management takes note of who delivers; it takes a while to get noticed, but once you are you get all the high-profile projects.
There's nothing (unless it hasn't been invented yet) that can't be implemented in software in a silo given infinite time, but the ability to deliver complex solutions to difficult business/process problems that require buy in and coordination from a lot of people are probably these kinds of projects, particularly if these projects are alterations or additions to other pieces of complex processes that already exist and are hardened but need improvement or overhaul.
Here's an example from my work. We use a legacy version control system alongside git. This causes tons of issues and the way forward would be to deprecate the legacy version control, but doing so without disrupting current engineering work and making tangible improvements going forward is a very complex task that spans a whole lot of teams and is risky and tricky to implement