On the moral epistemology side, one view is that we can know basic moral beliefs by moral intuition, called Ethical Intuitionism. For example, Michael Huemer's Ethical Intuitionism (2005). This can be a form of foundationalism, where moral intuition constitutes non-inferential justification for moral beliefs, a moral sense of sorts. If this is correct, then Hume's is-ought thesis is simply irrelevant, as we do not need to derive moral truths from descriptive truths.
There are also some fun logic tricks you can play to at least partially get around Hume's law. For example, a disjunction introduction of the form: A, therefore, A or B, where B is an ought. For example, the sky is blue. Therefore, the sky is blue or I ought to go punch my roommate. These are fun but do not really get fully moral conclusions based on fully descriptive premises. You can run similar examples with stuff like the paradox of material conditional or "All xs are ys. If xs ought to A, then ys ought to A."
When it comes to moral ontology, probably the most extensive defense of an explicitly atheist moral metaethic is Erik Wielenberg's Robust Ethics: The Metaphysics and Epistemology of Godless Normative Realism, a view sometimes called moral Platonism since it affirms abstract objects of moral significance. You can watch a debate between Wielenberg and William Lane Craig on the topic or read their book that came out as a result of the debate (with additional commentaries) A Debate on God and Morality: What is the Best Account of Objective Moral Values and Duties?
Finally, many of the arguments for moral realism/objectivism do not contain God in their premises, so atheist ethicists have no problem affirming that there are objective moral truths. (Note that moral realism/objectivism typically includes the rejection of error theory built in, so they affirm there is at least some objective moral truths and thus nihilism is false). Some arguments would be Terence Cuneo's (and many other's) companions in guilt arguments, David Enoch's indispensibility argument, Michael Huemer's ontological argument, etc. Also, I know there also have been specific arguments against the idea that morality has or needs a "source," but I am not that familiar.