Okay, I will generalize that one and then answer as a Western strong skeptic:
Can anyone prove that their claims of objective reality are true and that their beliefs are justified and warranted?
No, proof, truth, justification, warranted and also those other words are a part of a classical Greek attempt to use rationality to explain objective reality. It failed and that is why today you get this:
Philosophy of science - Wikipedia
Notice the first part: "All scientific study inescapably builds on at least some essential assumptions that are untested by scientific processes.Kuhn concurs that all science is based on an approved agenda of unprovable assumptions about the character of the universe, rather than merely on empirical facts. ..."
The notion of all these words are no different than religion in effect. Truth comes in at least 4 variants and then you get cognitive relativism:
Cognitive Relativism | Internet Encyclopedia of Philosophy
Historically the classical Greeks tried to do without authoritative religion and rely on democracy. That lead them to try to figure out if truth and all that could be used?!! It can't and that connects to modern human rights. It is the reason how human rights are the declaration of human rights and not the proof and truth of human rights.
As a skeptic I don't do standard religion or do I do standard truth and all that. Just as I don't need religion I don't need standard truth, proof and what not.