Well, in Safari, open Settings and on the General tab is an item "File download location" where you can select how you want it handled. I use "Ask fo reach download" so that if I want, I can redirect, but the setting will remember the last location you picked, so once you designate the Desktop, it will remember that until you pick somewhere else.
If, like me, you are a digital pack rat and download stuff/leave stuff in the download folder for a while the desktop can get crowded. I suggest choosing whichever of the following methods fits your workflow best.
1. Set Finder to show the sidebar in each Finder window and make sure the Downloads folder is in the sidebar.
2. Put an alias to the Downloads folder on the desktop and direct Safari to the alia. That should put the actual file in the Download folder but it's easily accessed from the desktop.
3. Create a folder on the Desktop and direct browsers to put things in that folder.
And in Google Chrome if you use that, its setting and downloads options choice is set in its Preferences window unless they have changed with a later version than what I use.
Shop for your Apple, Mac, iPhone and other computer products on Amazon.
We are a participant in the Amazon Services LLC Associates Program, an affiliate program designed to provide a means for us to earn fees by linking to Amazon and affiliated sites.