There are lots of niche medical investors, as well as government grants. You can try to pitch to those. They'll also understand and be able to criticize the idea better.
You can sell it to a hospital before you build it. Pitch the product, get feedback, then build. If the problem is big enough, they'll pay you in advance.
Also, in rare cases, depending on your pitch and network, if the customer (hospital in this case) is impressed and gives you the order, you can ask for a token amount which can help you get off the ground and work towards the product in discussion.
I wouldn’t call this a rare case. It’s a pretty common strategy in enterprise b2b startups. You develop a PoC that solves a real problem for customers with real money, and they’ll pay you to be one of the first customers if you can implement their feature requests.
You can sell it to a hospital before you build it. Pitch the product, get feedback, then build. If the problem is big enough, they'll pay you in advance.