You don't have to prove a negative, but if you want real trust from actually paranoid people, you will have to give up keys to the kingdom and work hard for it.

All your software/hardware would need to be open source, you would need to be regularly audited by neutral third-parties, actively work with the community to provide paranoia-level ongoing transparency reports and continuous improvements that the community wants to see, be willing to adopt many suggestions given by smart people, and just in general stop using your words to tell people you're serious, and use your actions to show it.

If someone says they are skeptical of XYZ, ask them what they would accept as proof, and then provide it.