I know this isn't your intention, but I think this logic kinda amounts to sophistry, and won't really assuage anyone's fears about whther atheism implies nihilism. If meaning is arbitrary, then it is vanishinly meaninful - like multiplying by zero. It's like playing a game with somwone who changes the rules whenever they are losing.

But I think there's a better answer.

If you hop in the shower, do you care if it's ice cold, or if it's warm? Of course you do.

And the fact that you care, means it's meaningful to you. Inherently. And it's things like that - things that we care about - that are absolute, undeniable proof of life's meaning.

So anyone says that life has no meaning, or that atheists believe that life has no meaning is wrong. Simply because we bear witness to the inherent meaningfulness of life every moment of every day, by the fact that we care about, if nothing else, how we feel.

There's more conversation to be had after that of course. But that's the starting point - the fact that we can't help but care about how we feel. And the fact that, presumably, every sentient being anywhere in the universe is going around caring about how they feel all the time.