It has been reliably estimated that must plastic in the world's oceans doesn't get there directly - it is flushed down an amazingly small number of big rivers. In fact 90% of the plastic in the ocean got there by travelling down only 10 rivers (usual suspects: Yangtze, Indus, Mekong etc). So all we need to do is clean up ten rivers. That may be hard but it is in no way impossible.
Many environmental problems are framed in a way that makes them seem insoluble except by a thunderbolt from Zeus or other unlikely and idealistic solution. Yet by looking at a 90% solution we can see a way forward in many cases. The old dicta that 90% of the problem is caused by 10% of the population (otherwise known as the 90/10 or 80/20 Pareto principle) can be turned to the advantage of pollution controllers. Find out who is causing 90% of the trouble and focus on them.