First of all, that depends on the browser. If you make your own one, using the open source chromium from https://github.com/chromium/chromium it can be yes, depending on what you program.
If it’s not in the settings of the browser you use, the answer, alas, is no.
I checked Firefox. It allows you to specifiy a program to open the downloaded file with a certain extension. If you use a program that opens the file and deletes it, it’s only on your PC for a very short time. But few users would set their setting to delete a file they download, so it seems a quite useless setting. There is no way to specify it in the Windows registry or in a policy, so that you as a system manager can set it, and the ordinary user can’t undo it. That’s for the simple reason that commercial browsers are made to run in other OS’es than Windows.
Feel free to ask Microsoft to add the option to Edge in such a way that it can’t be overwritten by non-administrator users in your company network. But sorry if using Chrome is the company standard.
My advice to avoid ransomware is to only download from trusted internet sites/sources and not to randomly click on links that you see on the page but don’t know/trust. A little due diligence goes a long way. Sometimes you cannot rely on someone or something else to do it for you.