Although the Windows 10 May 2020 Update, version 2004, was originally launched on May 27, 2020, it hasn’t been available for most devices through Windows Update due to several issues that can cause problems during and after the upgrade. However, after the release of the Patch Tuesday for June, the rollout of the feature update is expected to expand to more devices.
While the new version should now be available for more users, the company still limiting the release to only devices running version 1909 and 1903. However, the new announcement indicates that more systems, including Surface devices and from other popular brands (such as HP, Asus, Dell, Acer, Lenovo and others) should now be able to receive version 2004 when using the Check for updates button in the Windows Update settings page.
You can always use these steps to find out whether your hardware and software configuration are supported. If you have a device from Dell, you can check in this support page (via MSPowerUser) to determine the computers that Dell has tested to be compatible with the Windows 10 May 2020 Update. If you have a Lenovo device, you can check whether your hardware is compatible with the new update in this support page.
If you don’t receive the message with the option to download and install the update, you shouldn’t try to upgrade manually using the Media Creation Tool or Update Assistant as it’s likely to result in problems during and after the installation.