Поезд прибывает в данный/настоящий момент.

*скоро

Не понимаю... А в чем тогда разница между presently и soon/shortly?
Я бы подумал, что поезд уже находится в процесси прибытия, т.е приехал, но еще не остановился полностью.

When PRESENTLY means NOW, it normally comes before the verb: The train is presently arriving. The thing is that with verbs of motion, the -ING form is commonly used for the future, so your sentence already has a future interpretation to the native ear right out the gate, so that — coupled with the position of PRESENTLY — mean: The train will be arriving SOON/ANY MOMENT. In this context, you can also use DIRECTLY to mean SOON.

Look at the examples in this entry: https://www.vocabulary.com/dictionary/presently Note the position of the adverb in each example.

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