Amazon's market cap at close today was $438 billion.
To match Google's earnings multiple, Amazon would need something in the ballpark of $14 billion in net income.
They're chugging toward $200 billion in sales. $14b in net income off of that is very reachable. Even if we apply a much more conservative premise to it, they're still growing above 20% - maybe it takes them $280b in sales to get to $14b in net income; they're going to get to that sales level within six or seven years plausibly. AWS alone is all but guaranteed to generate $5+ billion in operating income within a few years. The issue isn't whether Amazon will one day justify ~$400 billion, as that's very likely, it's how far from the future are the gains being pulled. 3 years? 5 years? 10 years?