The surface area of Earth is over 510 million square kilometers. With a post distance of 0.25km, there would need to be sixteen times that number of points. Using 8.16+ billion (10^9) points is not a viable solution to this problem, even after reducing it to land area in populated continents drops you close to the 2.1B row physical limit of file geodatabase.
The accepted answer generated a 25km x 25km grid in "4 minutes". If generating an 0.25km x 0.25km grid held to that performance velocity, it would take 40,000 minutes (roughly 28 days) to complete the raw grid. Adding point-on-land tests for each vertex would increase runtime by two or three orders of magnitude, but with some algorithmic cleverness you might get cluster-of-points-near-land evaluation to only a single order of magnitude, which now places you at 280 compute-days for creation.
Rendering 60M points takes several minutes. A full table scan on 2000M points can't take less than an hour.
I try to avoid more than 20M features in a table --100 times that is too ugly to contemplate.
I would suggest that this is not feasible without making significant design changes (altering either the post interval or somehow utilizing multipoints to reduce the feature count, or both).