The triggered ability will resolve before Bygone Marvels does. If Bygone Marvels is countered in response to its own triggered ability, you will still copy Bygone Marvels twice.

Some descend triggered abilities include intervening "if" clauses (i.e. "if you have [four or eight] permanent cards in your graveyard" in the middle of the ability). Each of these abilities checks your graveyard at the moment it would trigger to see if it does. If you don't have the required number of permanent cards in your graveyard at that time, the ability doesn't trigger at all. If it does trigger, it will check again as it tries to resolve. If you don't have the required number of permanent cards in your graveyard at that time, the ability won't resolve and none of its effects will happen.

Cards with the ability word "descend N" have abilities that care if you have at least N permanent cards in your graveyard.