Atheists do not claim that life has no meaning or purpose - just that life does not intrinsically come with it.
Let's say a person gets a paid week vacation, without any plans of how to spend his or her time. It does not take long before this person spontaneously figures out what to do with him or her self, whether its painting a room a new color, or catching up on some research. We're perfectly capable of coming up with meaning and purpose on our own. That counts for anyone.
Atheists just don't have it handed to them on a silver platter.
Additionally, there is a shift in focus. What tends to matter more is the journey itself, not the end-destination. Even if in 10 million years, no one remembers you, that does not really matter to your ability to enjoy the life you have now, and make the best of it. It is a matter of attitude towards existence.
It is like asking, "How can I have any self-esteem if I don't have the President of the United States telling me that I'm special?". It may be difficult for such a person to comprehend an emotional infrastructure that does not involve an influx of compliments from others, but many people are fully capable of having good self-esteem whether anyone is complimenting them or not. It is all up to you - it is your decision what sort of attitude you take towards life, whether it is self-esteem, or a sense of meaning and purpose.