Ya there are, but it's such a vanishingly small percentage that it's not material.
There's good stuff like Y Combinator, and I was excited when it started because it seemed to grok that the fundamental problem in startups is that first $10,000. But (and this may be a controversial opinion) I feel like they fell into the same trap that every other incubator falls for, which is catering to elites. Now it seems to be a bit gamified, filtered through the lens of a certain youth demographic pitching to wealthy investors for large sums of money ($125,000), like the show Shark Tank.
I would very much like to see something that looks more like the grant system you mentioned, where small amounts of money could be obtained with relatively few hoops or strings attached. I've had countless times in my life where $5,000 or $10,000 would have given me the runway that I needed to finish a project and make money. But the money never came, so those all ended in failure, and a person can only fail so many times into midlife before playing the game itself feels like failing. If I knew in the 90s what I know now, I maybe wouldn't have chosen tech as a career.
The flip side is that I've survived on almost nothing for so many years, that I feel a calling to work towards providing income to everyone, everywhere. I think that's something we can manifest if we go back to first principles. I'd propose studying the history of such attempts and discovering which steps of the process were sabotaged by external pressures, then routing around that interference. Basically a startup working to solve the problem of income. The fact that this sounds at least a little preposterous seems more like of a failure of capitalism to me, than something fundamental.
A practical attempt at this might look like building solar farms to power cryptocurrency mining, to route around the problem of energy markets not buying alternative energy from homeowners at the going rate. Every market has that kind of defect that can be exploited. But they're difficult to see when we're at the losing end of the bargain as consumers, or dependent on the cashflow they generate as employees.
I might be slightly bitter after watching no movement on this in over 25 years, so please take what I'm saying with a grain of salt. I'm also super-optimistic about stuff like solarpunk :-)