Split it into 6 x $500 or 3 x $1000 and DCA every week.

If you want to have your BTC non-KYC (it means not connected to your ID), then use non-KYC p2p exchanges like Bisq, HodlHodl, Peach Bitcoin or Agoradesk.

You may also want to check out Azteco vouchers.

Good luck and feel free to ask.