Starting June 6, 2019, Windows 10 version 1903 (May 2019 Update) is fully readily available for anyone through Windows Update. Although the May 2019 Update was officially launched on May 21, 2019, it was only available for any select number of devices through Windows Update, but now it's available more broadly.

According to the Windows 10 health dashboard website, version 1903 has become readily available for anyone manually when clicking the Look for updates button starting June 6.

However, when checking for updates, your pc won't upgrade immediately. Instead, you'll get a new "Download and install now" choice to imitate cellular phone manually, because feature updates no longer apply automatically on computer unless you're running a mature version.

If you're currently running the Windows 10 version 1803 (April 2018 Update) or older, at any time, Windows Update will try download and install the new version automatically. If you're not prepared for the new update, you are able to prevent this using these steps.

In case your device isn't the getting the new version, you can use alternative upgrade methods:

Windows 10 version 1903 clean installation process
Windows 10 version 1903 upgrade using Media Creation Tool
Windows 10 version 1903 download using Update Assistant