The answer is yes, if you'll grant me some reasonable assumptions.
Generate a random seed (uniformly at random), then use a cryptographically secure pseudorandom generator to stretch it to an arbitrarily long sequence of pseudorandom bits. Under reasonable cryptographic assumptions, that pseudorandom sequence will be computationally indistinguishable from true randomness and so will be just as good as real randomness.
The cryptographic assumptions required are widely believed to be true, e.g., that AES is secure. The likelihood of a practical break of AES is almost certainly far smaller than the likelihood of a bug in your code -- so from a practical perspective, it's in the noise.
From a theoretical perspective, the situation is different. This answer is only implemented at practical implementation, not at proving theorems about complexity classes.