TLS is used for protecting the communication between client and server. The application data are encrypted with keys which are unique for each connection and which are created during the key exchange part in the TLS handshake. The key exchange is constructed in a way that both input from client and server is used to create the keys and thus no side has full control over the encryption keys.
The recommended key exchange method is Diffie-Hellman and this is also the only one which is available in TLS 1.3. No private key of the server is even used during the key exchange and thus the private key of the server does not affect how the data gets encrypted. This also means that there is no way to pre-encrypt the data by somehow using the private key. The private key is only used for authentication, i.e. to make sure that the client is actually taking to the correct server.
And while in the older RSA key exchange method the private key of the server is involved to protect the exchanged key it does not influence which key gets created and thus pre-encrypting the contents is not possible in this case too.
In other words: the main point of the private key is to provide authentication to make sure that the client is talking to the correct server. This authentication is done by signing some kind of challenge with this private key and thus proving ownership of this key. Since this challenge is unique for each TLS session the server must actually somehow have access to the private key and cannot just offer pre-signed content.
Still, you could use a certificate in theory to sign all the static content you have and you could then transport this signed content over plain HTTP. This would not protect the content against sniffing but it would protect it against manipulation. While this kind of protection is outside of TLS you can find something like this for instance in mail (S/MIME or PGP). Still, it needs a client which will verify such signatures but there is currently no such client. But there is actually an internet draft which goes in the direction of what you want: Signing HTTP Messages