Presuming you mean in New Edge, the Chromium-based one, and you can determine that's what you're using by hitting ALT+F, and if the menu opens you are. If it doesn't, and you hit ALT+X, that's the Old Edge which should be ditched at this point.
Changing the Search Engine in Chromium-based Edge Browser
What follows presumes you have Edge open and have focus on that window:
1. Hit ALT,Down Arrow or ALT+F to throw focus to the Edge Menu button and expand the menu itself.
2. Follow that with S for settings. This will open a tab showing the following address: edge://settings/profiles
This is the Edge Settings page. One could also just open a tab and paste in the address above, but it's better to know how to get there via the menu button.
3. Tab once to land on the Profiles item in the Settings tree. Down arrow once to get to the Privacy and Services item, then hit Enter to get that pane to load.
4. Hit Tab to throw focus into the pane. Hit CTRL+F to bring up Find, then enter Address as your search term. Hit Enter to run that Find.
5. The Address Bar entry text will be found. Hit escape to close the search, then Hit Tab once to land on the actual button for same and activate it.
6. You're now in the Address bar settings, and there are three controls there, the titles of which are pretty self explanatory. To set your default search engine in the address bar, use the setting for that. To change your default search engine for the browser, go to the last option, Manage search engines, then:
a) Tab once to land in the search box.
b) Start typing the name of the search engine you wish to use. If it's one of "the big ones" like Google, Bing, Yahoo, DuckDuckGo, etc., it will very likely be the only search result returned, but sometimes it isn't.
c) Hit TAB three times. If your preferred search engine is what you've landed on move to step 7, if it isn't, then down arrow through the results until you land on the search engine you want.
7. Right arrow three times to land on the "More Actions" button for that search engine and activate it.
8. This will bring up a pop-up menu, with "Make default" being the first item. Since that's what you're trying to do, activate that option.
You're done. You can close the settings tab.--
Brian - Windows 10 Pro, 64-Bit, Version 1909, Build 18363
The purpose of education is not to validate ignorance but to overcome it.