The earlier you start, the greater the risk of cold weather. In an average year, you'll be cold at times but okay. But there's always a chance you'll have to wait out some snow a day or two in the high country. And you may get to McKenzie Pass in Oregon before it opens, but Santiam Pass is available as an alternative if that happens.
An April start will require you to bring more cold-weather gear than a May start would.
Also, the earlier you start, the greater the risk of campgrounds that haven't opened yet. Not a problem of course if you don't plan to camp.
Nobody can predict the weather that far out, so it's all a probabilities game. We all have constraints we have to live with, so we can't always pick the time with the lowest risk.