Solo: A Star Wars Story may be fresh in our minds (well, some of our minds), but the Star Wars machine has no off switch. Fans will have to wait until December 2019 to see the conclusion of Star Wars: Episode IX and the conclusion to the Skywalker saga as a whole. After that, it's anyone's guess what's next on the list, but Rian Johnson's new trilogy will no doubt be near the top of Lucasfilm's to-do list. As to when we can expect to see the first movie in the series, it won't be anytime soon, but producer Ram Bergman just gave a tentative window of two years.
Before Star Wars: The Last Jedi was released, Lucasfilm decided to give director Rian Johnson the keys to the kingdom and announced that Johnson would be creating an entirely new series of Star Wars movies completely divorced from the Skywalkers and all their drama. It was exciting news, but we've still got plenty of time before the first movie makes it to theaters. The project is still in the very early stages of development, so it's likely not coming to theaters too soon, but producer Ram Bergman, who worked on Last Jedi and will be producing the new trilogy, told From The Grapevine that the first movie could be arriving in two years.
Lucasfilm likes to release one Star Wars film a year. This year it was Solo and 2019 will cycle back into the main series with Episode IX. Assuming that the studio follows the same pattern, a spin-off film will release in 2020. (Perhaps it will be about Boba Fett or the rumored Obi-Wan prequel?) Then, potentially following that we could get the new film in Rian Johnson's trilogy, unless Lucasfilm and Disney decide to forgo the spin-off and get right into the new stuff.
Keep in mind that Johnson is creating all of this material from scratch so it could take longer to pin down, as well. Ram Bergman also said:
Writing a regular Star Wars movie with all the characters in place is already hard enough, so I wouldn't be surprised if Johnson takes his time in the scripting process to make sure that everything works before the studio commits to filming anything. Regardless, we've got a fair amount of waiting to do before we can expect to learn more concrete details about the project.
In the meantime, there's a Star Wars film our right now! It's called Solo: A Star Wars Story, though, perhaps you don't have much interest to go see that one based on its performance domestically.