The universe appears to have appeared from nothing. Why does something exist, and not nothing? This is about why, not how.
If no answer to, "Why does anything exist, rather than nothing?" is satisfactory, then is the question well-posed in the first place? I don't mean this as an objection to you asking the question specifically: I mean to ask whether the word "existence," on this level, has a stable value.
Or, then, we all might as well ask, "What is the explanation for the existence of explanations?" and hope for a non-circular reply (which hope will be dashed instantly and entirely). Alternatively, we can separate the issue into levels or orders: "What is the lower-level explanation for lower-level explanations?" is then not well-posed, but, "What is the higher-level explanation for lower-level explanations?" might be better. (And so on with, "What is the even-higher-level explanation for higher-level explanations?" ad indefinitum.)
Note that the SEP article on nothingness at one point frames the issue as one of why our world is not a concretely empty one:
Van Inwagen’s answer is that we are actually interested in concrete things. ... All material things are concrete but some concrete things might be immaterial. Shadows and holes have locations and durations but they are not made of anything material. There is extraneous light in shadows and extraneous matter in holes; but these are contaminants rather than constituents. Cracks can spread, be counted, and concealed. Once we acknowledge the existence of cracks, we get an unexpected transcendental explanation of why there is something: If there is nothing then there is an absence of anything. Therefore, there exists something (either a positive concrete entity or an absence).
Ontological pluralists do not dismiss this proof as sophistry. Kris McDaniel (2013, 277) thinks the proof is trivially correct. To address a more interesting question, McDaniel follows Aristotle’s principle that there are many ways of being. From the pluralist’s perspective, debate over whether holes exist is equivocal. The friends of absences use a broad sense of ‘being’. The enemies of holes speak from a higher link in the chain of being. From this altitude, holes depend on their hosts and so cannot be as real. Alexius Meinong’s talk of subsistence alludes to the lowest level of being. “Why does anything subsist?” is a perfectly legitimate question, according to McDaniel.