I don't think it will be soon. The hype around doge is huge, but there is a lot of resistance. Another big problem is hamsters - a few bad news and the doge will go to the bottom. Although, maybe Elon has already come up with something and doge will be on the moon.
It doesn't have to be soon. The important thing is that sooner or later Elon will start pumping the DOGE price again, whether it will be in half a year, in a year or even in a few years, it is certain that sooner or later the DOGE will reach the $1 level. HODLers will win again!
I wouldn't trust that idea easily. If Elon feels like it, maybe yes, but there is no certainty for that. He might choose another coin. Nobody knows how much he holds or if he is holding any DOGE at all right now.
Elon is most likely protecting his reputation, and you can bet that many people will be upset if they discovered that he is merely playing with the market. So I doubt Elon would choose any coins, and that's why he just chose Dogecoin: it's a meme coin, and he doesn't want to be associated with other coins, no competence. When Elon is shilling, he is well aware of his potential and impact on the market, and he will, of course, make the smart move; he is a clever man, after all, and that is how he became a millionaire.
Sooner, I'm sure that Dogecoin will hit 1$, just wait for a week or months, it will show us its potential.