A professional resume is the best investment you will make in your career, do you agree?

The actual question should be: "Do you believe a resume is everything?" The main investment in your career is yourself, your life.
You have to coach yourself to always keep up your self confidence, because without it, you can have a professional resume, but once you've lost your confidence, every opportunity is flying away from you.
With confidence, everything comes along, education, spirituality, good job, rewards and the joy of achieving the best of yourself and then you will reach to the best investment, that not only you make in your career, but in your entire life.

sure

Building a strong business relations and connections is also important

A professional resume do plays an vital role .But more important is that whether you are professional enough to own a professional resume .
To be called for the interview depends on resume but to get selected for the job it depends on your performance and experience .
So your experience is biggest investment of your career .

We can say one of the best investments.
I agree with Alexandra that your main investment is yourself.
Your resume serves as a catalogue or brochure of yourself, advertising your expertise, knowledge and skills, highlighting your achievements and experiences and detailing what you can bring to the table that others can't.
An excellent resume will make you become more marketable than other candidates.
It also creates a good and lasting impression from your potential employer.