The macOS Catalina Installer app is a 5 GB file. It will take a considerable amount of time to download, even in the background and depending on your ISP download speed. If it downloads in the background, when the download finishes, the app will open by itself and present front & center for you to allow it to install Catalina or to quit the app to install later. As His Foulness, the Croc God has said, the Installer app will appear in the apps folder when the download completes.
Believe it or not, we get this type of cry for help often because these are huge files and take a long time to download, especially if your ISP has restrictions or throttling for downloads. Keep in mind that Sierra or High Sierra* are also huge files and will take a long time to download.
Meanwhile, have you prepared for the upgrade? Have you made a backup in case disaster prevails? Have you perhaps run 1st Aid on your hard drive to make sure that there are no issues before you install. Have you surveyed your 32 bit apps for replacements since none of them will function on Catalina?
*If your Mac will run Sierra, it will run High Sierra as well.