Build USB 3.0 hardware H264 encoder with USB or RTMP output

Hello, I'm looking for help designing an encoder that would take video and audio input from a USB 3.0 connection, compress the audio/video into H264, and either expose a USB connection that would allow a program (such as FFmpeg) to take the compressed data over usb and stream it to a website, or would be able to directly send out an RTMP stream to a website using an onboard wifi connection. The video would be at a very large resolution: 3840x1080, and the compression would have to be fairly strong to preserve the visual quality while still producing a fairly small bandwidth. This could be done with whatever hardware you think best fits the task. Thanks for reading my listing and please reach out with a quote if you think this would be a good fit for you!