Being one of our founding engineers, I have several times identified a need and implemented a solution without "seeking permission" first. When I do want more formal company backing to pursue a project, a conversation with my manager or an email or a one-page Google Doc all sound easier than writing and submitting a grant proposal.
As our company has grown, I have seen my role change, and I have collaborated with my manager to determine a new direction and title for myself. Notably, I tried management for a while, and I ultimately decided to return to an individual contributor role (no direct reports). It didn't sound like Dr. Fratantonio had the option to stop mentoring other PhD candidates.
Freedom is not exclusive to founding engineers. Our company has a prioritized list of features available for development, and devs have a big role in choosing the next feature they work on, even when it's not a current area of expertise. Established engineers and new hires alike have a lot of latitude to pick technologies, architect a solution to a problem, implement a novel algorithm, etc. One relatively junior new hire is embarking on a project to rewrite much of our frontend code, with support from all of us.
Again, that's why I commented. Depending on what type of freedom you're seeking, industry may offer it and pay better and have better working conditions to boot.