Can a new Amazon seller get the buy box?

If you are doing FBA, new sellers always have the buy box.

Yes as a new FBA seller you can easily have buy box as the amazon favors new sellers as compared to old ones.

Yes, The buy box is always available to new sellers if they are doing FBA.

There is no guarantee that you can Win Buy Box even if you are an Old Seller because no one exactly knows how the amazon Algorithm works but there are some speculations on the basis of expert experiences that if you have a good selling history, good shopping speed, competitive price and FBA listing then you are more likely to win Buy Box. But still, there are some cases in which new sellers have the Buy Box.