Injuries are not normal or expected regardless of when you start. The important point is to use good technique and progress slowly. Hire a qualified personal trainer or coach to show you how to do it right. And don't try to do too much too fast. Your muscles will get stronger faster than your tendons and bones, so just because you can lift a heavier weight or run at a faster pace doesn't mean you should. Take a few months at your current level before trying to move up.
It’s both expected and normal, however, yes, as you point out, going slowly will give your soft tissues time to adapt to the new stresses you’re putting them through.
Just need to work through physio and be patient with it. Pushing through the pain will just lead to more pain that takes longer to heal.