While the Government is a trustworthy client - meaning that they pay their bills, getting in and building the trust necessary to clear the regulatory barriers in place, is a substantial challenge. Selling directly without an established base of paying customers and high-profile success stories is exceedingly difficult, sadly.
Networking, as some HN commenters mentioned, is one step - but procurement networking events are littered with hundreds of bright eyed entrepreneurs seeking to secure a government contract.
Bidding through the RFP process is another route - but often takes a very, very, long time, and could outlast the life of the company.
Another option is to capture the attention of a lawmaker or administration official who is looking to solve the very issue you have a solution for. I.e. they have a lot of constituents who are concerned about early disease warning systems and therefore they want to find a solution that disrupts the status quo.
Depending on how deeply you care about this issue - you could also seek out a fellowship (via tech congress or another non-profit seeking to increase tech’s engagement in government) or look to participate in the digital service (which is a non-partisan group of civic minded technical experts who are just looking to make government work better).