Sure it is. You just need a one to one function from person to [0, eight billion]. Use that as your array index and you're golden. 8 GB is overkill, really, you could pack some boolean datum like "is over 18" into bits within the bytes and store your database in a single gigabyte.
Writing your mapping function would be tricky! But definitely theoretically possible.
I'm old enough to have built systems with similar techniques. We don't do that much anymore since we don't need to, but it's not rocket science.
We had spell checkers before computers had enough memory to fit all words. They'd probabilistically find almost all incorrect words (but not suggest corrections). It worked fine.
Writing your mapping function would be tricky! But definitely theoretically possible.