If I'm understanding this correctly, the Palo Alto PA-220 allows for SSL/TLS traffic decryption using its proxy feature. By generating a Certificate Signing Request and loading it into the firewall, Clients should never receive a browser warning when accessing HTTPS sites?
You misunderstand how TLS works.
A certificate signing request is exactly what it sounds like: A request for a certificate authority to sign a certificate. The request alone is worth nothing. Compare that with the request to be released from prison, compared to a signed pardon letter.
As Z.T. pointed out in a comment, the requests needs to be signed from a certificate authority.
You have two ways of going about this:
For outgoing traffic
Your company should have an internal certificate authority, which is rolled out automatically to all clients using your endpoint management system. Then, the proxy can generate a private key and a CSR, and the IT department can sign the CSR with the private key of the internal certificate authority.
It is typically then configured that all outgoing traffic from employee hardware is rejected and required to pass through the proxy.
For incoming traffic
Since you mentioned that you don't want clients to install additional certificates, I assume what you want is to monitor incoming traffic. The proxy would then act as a reverse proxy, taking incoming traffic, inspecting it and forwarding it to the designated endpoint.
The setup is identical to that of your currently externally visible endpoint. You take the private key and certificate from that server and place it on your proxy. To the end-user's computer, this proxy is the endpoint. The TLS connection ends at the proxy, where the proxy can inspect the traffic.
The request must ultimately be forwarded to the endpoint (if deemed safe), and I recommend using an internal certificate for that, meaning you create a new TLS connection between the proxy and the endpoint. This has the advantage of making it harder for internal attackers to gather sensitive information from the communication between proxy and server.