How to speed up vertica's count query??

Put a live aggregate projection on it.
That way, the count is calculated as data is loaded into it.

But live aggregates don't support a straight count() (without a group by), so you'll need to pick something to group it by. I'd pick a low cardinality column, for example, country_cd. And then you could do count(), country_cd group by country_cd. To get the entire count, you'd just have to sum up the counts for all the countries. That would be ~100 rows, versus 280M rows. So, you'd be looking at something like 10 ms or something like that. Very fast.

Try making sure the stats on table are updated.
If stats is updated, then count should be faster.