Right, 900 million. How many ships would that take?
We can't say how many ships, unless we also know the timeframes involved.
In general, the Federation has some thousands of ships, but they are every thinly spread. For the Battle of Wolf 359, in Best of Both Worlds, they pulled together 39 ships, which were all destroyed. Major engagements in the Dominioun war had 600 to 1500 ships (not all of these were Federation vessels - the Klingons and Romulans were allied with the Federation.
So, for an effort like this, you can expect maybe a couple thousand ships?