Open yourself an account in the US and send the funds there so you can start trading / buying.
https://interactivebrokers.com/inv/e...p#open-account
This is a proper brokerage account and none of the fluff we have in NZ brokerage firms. Their commissions are competitive with again, none of the rip-off account management fees we see by NZ providers. IB also have brokers in Australia if you find having a US account is too far away.
Once your funded and ready to make your investment, the world is your oyster. But since your interest is specifically with Vanguard S&P500 ETF, it's ticker is VOO
https://finance.yahoo.com/quote/VOO
Since it's over $300 USD per share, you'll have to check if they do fractional shares. Also if you're only sending $20/week or so, then it may be a waste of time. I suggest to send much larger sums to make it worth while.