Let's say a wizard of second level has gotten themselves out in the middle of nowhere with no sources of food. Could they use minor conjuration to summon a loaf of bread, or a cookie? Or would taking a bite out of the food cause it to take "damage" ending the duration?
You can make it, but you won't be nourished
Minor Conjuration from the Wizard subclass School of Conjuration states:
conjure up an inanimate object in your hand or on the ground in an unoccupied space that you can see within 10 feet of you...The object disappears after 1 hour, when you use this feature again, or if it takes or deals any damage.
As you had stated, taking a bite of it would definitely constitute'taking damage' as it is no longer in it's original state. Once 'damaged', the object disappears which would include whatever you put in your mouth.
Also note that the Conjured object is clearly magical when observed (thanks @SirCinnamon!):
The object is visibly magical, radiating dim light out to 5 feet.