Word meaning "close in time, or presently happening"

Is there a word that can be used to describe something that is either close in time, or currently happening?

Something like "proximate" or "imminent", but without the implication that the thing has not happened/started happening yet.

Current

: presently elapsing (2) : occurring in or existing at the present time (3) : most recent

: generally accepted, used, practiced, or prevalent at the moment

Contemporary:

From the same time period, coexistent in time.

You nearly got 'em all already.

Without reference to the present, it would be: temporal-proximity.

With the context 'present,' it could be current.

And why not the elegant now? That can mean just what you want, perhaps?