Hello,
With no random generator at all, only a few cryptographic operations are possible: signature verification, hashes, MAC, symmetric decryption, symmetric encryption with a deterministic nonce.
If you have no entropy sources on the device, you can provision a seed during the device manufacturing, and use that for the random generator. In Mbed TLS, enable MBEDTLS_ENTROPY_NV_SEED, disable other entropy sources, and provide seed read/write functions as described in https://mbed-tls.readthedocs.io/en/latest/kb/how-to/how_to_integrate_nv_seed... .
The usage of the RNG is the same whether the entropy comes from a hardware RNG or only from a provisioned seed. You just have to configure the entropy module appropriately. Then you use CTR_DRBG or HMAC_DRBG or PSA normally.
Best regards,