I think that it's unlikely that trust in America is permanently gone because of what is recognized by increasing numbers of Americans, and by most of our allies as an orange swan; more pointedly as one aberrant flaming asshole.
I can also think of many versions of a newly elected president's reconciliation speech whose message would boil down to 'our bad, here's what I've said throughout my campaign and here are my now concrete proposals to fix things between the U.S. and those countries most of have never stopped thinking of as our friends and allies.'