No, the burden of proof lies on the side of whoever is making the positive metaphysical claim. As Wikipedia so neatly puts it:
The Fallacy of Demanding Negative Proof
Outside a legal context, "burden of proof" means that someone suggesting a new theory or stating a claim must provide evidence to support it: it is not sufficient to say "you can't disprove this." Specifically, when anyone is making a bold claim, and especially a positive claim, it is not someone else's responsibility to disprove the claim, but is rather the responsibility of the person who is making the bold claim to prove it. In short, X is not proven simply because "not X" cannot be proven.
Let's say I tell you there's a magical invisible unicorn in my back yard. I don't have any evidence of its existence, and you don't have any evidence of its non-existence. But that doesn't mean that "both sides are equally proven". The scientific method demands that the one making a positive claim defend their view with evidence.
Theism is not a 'lack of belief in the non-existence of god', because this implies that the default position is one of belief, and that from this, non-existence must then be proven. According to the burden of proof the opposite is true; the default position is one of lack of belief, and existence must be proven.
Also, the vast majority of atheists are agnostics.