Yes, you need health insurance for your stay in Germany with an EU Blue Card from the first day after entry. As a rule, you must already provide proof of this coverage when you apply for your visa. To bridge the time between entry and the start of your job, you should take out incoming insurance such as the WORK & PROFESSION Insurance.
Once you start working in Germany, you will have either public or private health insurance. If your gross salary is above the compulsory insurance threshold, you can choose. If your salary is below it, you will be covered by public health insurance.