Trion Worlds has sent out its first wave of Trove alpha invites today as the game moved into its latest phase of testing. On Reddit, Trion devs addressed how players may gain access to the alpha: "We will be inviting people both at random from the pool of everyone who has signed up as well as directly inviting strong Trove supporters: community contributors, streamers, and so on."
If you're not content to wait for an alpha or beta invite, you can cut the wait with a few bucks by purchasing one of Trove's new supporter packs. These start at $5 and go up to $2,500, with perks such as testing spots, in-game credits, in-game items, the soundtrack, and even the ability to help create a biome. Basically, $5 gets you the beta and $20 (on up) gets you the alpha, if that's what you're seeking.
Additionally, the more that the community chips in for these packs, the more additional rewards will be unlocked for everyone in the form of "bonus milestones."