Microsoft Flight Simulator is poised to leave alpha behind and fly over to closed beta soon. Microsoft and Asobo snuck the roadmap update into a development post last week (cheers, ResetEra) but didn't include a specific date. It's due to appear in mid-July.
The first technical alpha kicked off in October, but since then it's moved onto a regular, ongoing alpha that recently had its third update. There are just two more to go in early and late June, and then it's on to the closed beta. How it will differ from the alpha hasn't been announced, but you'll still probably need to sign up to the Insider programme.
If you've not had a chance to play yet, you can still live vicariously through the official and community screenshots posted alongside the development updates. To see it in motion, check out this recent footage of planes flying through its impressive volumetric clouds.
Before you plan your aviation adventure, make sure to take a look at the Microsoft Flight Simulator system requirements. The minimum specs seem pretty attainable, but you're probably going to have to make a lot of sacrifices. The ideal specs are a much bigger ask, recommending a RTX 2080 or equivalent. I'm sufficiently close to the ideal specs, but if I was ever going to upgrade for just one game, it would probably be Flight Sim.