How to Always Start Any Browser in Private Browsing Mode

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Private browsing mode doesn’t offer complete privacy, but it does prevent your browser from saving your history, searches, cookies, and other private data between browsing sessions. You can have your browser always start in private browsing mode if you prefer it.

Most people won’t want to use private browsing mode permanently. You will have to log into the websites you use each time you open your browser, as your browser won’t save the cookies that keep your login state.

https://www.howtogeek.com/137466/how-to-always-start-any-browser-in-private-browsing-mode/

As noted, you probably don't want to use private browsing mode all the time. Therefore, a strategy would be to have one browser, such as Chrome, start up in normal mode and another browser, such as FireFox, start up in private mode by default.