Could an inexperienced advisor hurt my career?

An inexperienced advisor can hurt your career by being relatively unknown. This means they may not have access to the same network and that their recommendation letters do not carry the same weight. Inexperience in supervision may, for example, lead to unrealistic expectations. Or an inexperienced advisor can be very good for your career, by quickly rising to fame with the awesome publications the two of you will write together and being fresh in everybody's memory when writing recommendation letters. They may spend plenty of time on working with you.

An experienced advisor can hurt your career by being never there. They may already have made their name, have extremely high expectations from PhD students, to the level of cause them to be overly stressed and quit. Or they may be very good for your career, as dedicated as can be to PhD students, prioritising them above most other duties, having realistic expectations from PhD students, and having great influence when writing recommendation letters.

Bottom line: an experienced advisor may be better for you than an inexperienced one, but that certainly does not have to be the case. And keep in mind: a very good/famous scientist is not always a very good PhD advisor.

One indicator of what you can expect is his publication record prior to his professorship. This is not a perfect indicator, but it's a starting point from which to evaluate his potential impact on your career. If he has published regularly and in good journals, and if his co-authors/former supervisor is well-known it could mitigate the fact that he is just starting his career.

Another thing to consider is how established his lab is, physically speaking. Are you going to be able to actually do research right away, or will the first year of work be mostly heavy lifting and setting up equipment before you can start generating data? If the lab is not yet set up, it can be a big risk.

All that said, having an advisor who is going to be highly motivated to publish and who you get along with are both huge pluses. If you get along well and are one of his first students you can probably count on a lot of support.

There's no really clear answer to this unless you actually linked his research profile (which you probably shouldn't do). Certainly starting with a young professor comes with risk, but if he is clearly motivated and you get along that can mitigate a lot of it.

There is no way that I would say, "Inexperienced? NO! Forget him!" But his experience is one factor -- among many -- that you should take into account. You want someone who will assign you work that will not only be interesting but will look impressive to the people you will eventually be looking to hire with. Also, you need someone who can advise you on how to navigate a job market that is often extremely competitive. And, yes, you want someone with connections. My own situation years ago was that I had an advisor who was actually quite well known, working in a European institution. But he didn't know enough about the US job market, which I would eventually have to go back to, to help me out at all in the ways I suggested above. I went back completely unprepared to find a job.

That being said, there are advantages to new guys -- energy, "young blood", inspiration, innovative ideas, etc. So there are many things to take into account. You just have to "sum up" everything and see whether the overall "total" is what you need.