If the US, or any European country, started letting Palestinian refugees in en masse, a lot of them would manage to get there. Egypt’s culpability here is the most salient because they’re physically closest; but I don’t see how that makes the country uniquely culpable for failing to prevent a preventable situation.
If the US decided to let all Palestinian refugees in -- This obviously wouldn't happen, but if -- we could definitely get boats with capacity for thousands of people a day to a pier that we built [0], get them to somewhere where they could buy flights or have people donate to a fund to pay for them, etc.