I am moving to California from New Zealand. Most likely in December this year. I have some US ETFs in my brokerage account, so the questions is if it's better to sell them before I move and then re-purchase. Would I need to pay capital gains tax in the US on that sell? Or US taxes would apply only from the date of my arrival to the US?
Consult a professional.
Consider moving in January, or at the very least not starting work in the USA until January 1st. Your tax liability may be small for the portion of your income that occurs in December, but it hardly seems worth the paperwork.
Also be aware that the IRS taxes several things that NZ does not. You are aware of capital gains tax, but if you have any self-employment income in NZ, the USA wants an additional 12.9% of that for Social Security and Medicare that is not covered by the Foreign Earned Income allowance. A clean break (and again, a clean break at the start of a new tax year) is well worth it.
It's also worth planning your exit strategy. Will you be contributing to a 401(k) or IRA? If you move back to New Zealand, is your custodian going to allow you to keep those accounts active (mine does not)? If you withdraw money from your 401(k) after retirement, is it going to be worth reporting all your world-wide income to the IRS?
FWIW, I first moved to the USA in December 1995, and stayed there 10 years. If I go again it will be in January.
If you are a citizen, you move abroad and keep your citizenship, the U.S. will continue to tax you.
If you give up your citizenship, you may have to pay an exit tax if their average annual tax based on the past 5 years of earnings as well as your net worth. The assets will be marked to market on the date you leave.
Understanding how tax law applies to you is often an exercise in futility. I read this article and it made my head hurt: https://moneymattersforglobetrotters.com/what-should-i-do-with-my-us-investment-accounts-when-i-move-overseas/ . I'd suggest that you consult with an account who specializes in this area.