On an iPhone you can also use Sign in with Apple, which skips the email entirely.
Once you are in, that device stays signed in. You will not be asked again unless you sign out.
If the link says it has expired
Ask for a new one. A link lasts 30 minutes and can only be used once, so an old email or a link tapped twice will not work — that is deliberate, so a forwarded email cannot sign anybody else in.
If the email opens in the wrong place
Some mail apps open links in their own little browser rather than in Safari or Chrome. If you land somewhere unexpected, copy the link and open it in your normal browser, or paste it into the sign-in screen in the app.