I'm not sure what a program like that could look like in practice, though. You could put money directly into peoples' pockets through a sort of grant-like application process, ("I want to buy $250 worth of resistors, capacitors, chips, wire, and breadboards to make a new kind of fitbit prototype") but that would be an easy system to game, and a lot of the costs associated with experimenting with theoretical ideas comes from equipment anyways.
Because not everyone can afford or find room for a scanning electron microscope or a CNC lathe, right? Many cities have hackerspaces, but their capabilities often stop at hand tools and working with thermoplastics unless you're very lucky. So what about universities? They're present throughout the entire nation, often already publicly funded, and have access to functional research and manufacturing equipment.
Sadly, my experience trying to get even a few hours' use of any sort of university equipment, whether supervised, paid, through night classes, or otherwise, has been met with absolute stonewalls. If you don't pay full tuition, you can fuck right off.
So I'm not sure what the solution here is. What's an average person who wants to get into science supposed to do, besides be independently wealthy?