How do you build reputation in that environment?
word of mouth and circle of trust that spread?
A good science should focus on verified and verifiable predictions.
No one will quote you if you don't have good reputation either.
> If 3rd party verification is the source of reputation, then how do you get started?
By surviving the check against the reality. Or doing 3rd party verification on other works.
Volume isn't really a problem going forward, at least in mathematics, since every proof can be accompanied by a Lean verification. Whether other disciplines can implement automated verification or quality assessment will depend on the details of the field.
Mathematicians need to rethink what is the purpose and value of doing pure mathematical research in the future. Until know, they have mostly valued the creation and systematization of human knowledge. From that perspective, Lean proofs mostly increase confidence in the human knowledge. But they don't contribute directly to it, as a formal proof is unlikely to contain insights that are not present in the human proof.