That so-called paradox takes the following assumptions:
• That it is possible for a region as large as even a single galaxy to ever be "full" of one species or their creations.
• That anything can keep spreading indefinitely, and remain intact, not only across the gargantuan distances involved but also over potentially millions of years for other species to encounter them.
• That intelligent life wants to keep spreading or exploring indefinitely. As opposed to, say, creating VR universes of its own and attaining contentment within them.
• That there are only a few "directions" into which species or machines can spread across the universe, for them to run into each other.
• That there are no "stabilizing" forces – natural or adversarial – which counter rampant expansion.