I think it's a choice you make and it's a choice that you live with, and you won't know if it was 'right' or 'wrong' till something does or doesn't go wrong.
I do both - insure immediately and for the early years, when any congenital issues will become apparent, accidents are most likely, and premiums are low. Be sure to choose a reputable lifetime policy just in case - if you change insurer previous health issues won't be covered. Meanwhile build up a savings account for later years, when premiums soar.
Thank you for the input. It's terrible that they started denying claims for you. I guess I need to read a little more into the detail of the insurance I was considering. It's called Figo (relatively new company I think and had good reviews).