The une fois structure doesn’t work quite like “once” in English.

Une fois la barre de progression rose disparue, redémarrez l’appareil pour terminer la mise à niveau.

As Feelew writes, quelques could be replaced by plusieurs. (I think quelques connotes that it’ll be “only a few”, whereas the English usually reads like an invitation to go make yourself a cup of tea.)

Le processus peut prendre plusieurs minutes.

You can also trade the “can” of peut for the “could” of pourrait, though both seem okay to me here.

Le processus pourrait prendre plusieurs minutes.

Those are my suggestions. I’m open to anyone else’s if they want to comment them.

Edit: Also, noting the comments below, if you give some extra context as to what sort of upgrade it is, we can help decide if the various terms are perfectly right (type of process, significance of upgrade…).