You probably won’t launch an entire product line out of your own sheer will, but you can totally push for smaller scale work. Push for creating a tool to improve your team’s processes, or push for a few feature within an existing product. Focus less on the “entrepreneur” aspect and more on the “build fun and autonomy into your work” aspect. If you’re trusted and respected within your organization, you’ll probably be able to push through ever-larger projects (assuming they’re not net-negative). This probably isn’t a working strategy if you’re within your first year, but if you’re a respected senior engineer who wants to scratch an itch, you’ll probably have much more success.
Or, if you work at Google, push for a new chat app. It’ll probably be approved.