My dad negotiated contracts for the DoD for 15 years, and he taught me to negotiate hard on a car. Have gotten some amazing deals over the years, but I haven't tried since Covid. Still, I'd stick to the tried and true:
1. Do your homework. Know how much the car should cost, both baseline and out the door.
2. Never open with your final number. Always start with a lowball (but not too low, or they won't take you seriously). This gives you room to negotiate.
3. Always negotiate on the price of the car, not payments. Best to secure your own financing before you go, but dealer financing is okay as long as you don't get distracted by payment talk.
4. You said you're not trading in, but for anyone reading along who is: Always negotiate the trade-in separately. Never, ever, ever let them roll the trade-in into the negotiation. Stick to the sales price of the car first.
5. If you have someone who can go with you, the good cop bad cop routine works brilliantly. One of you play the role of sympathetic to the dealer, totally understanding of whatever they tell you is a reason they can't lower the price. The other has a choice: Play hardball and reject all the arguments or, if you can pull it off, play clueless. Pretend you don't understand what they're telling you, and substitute your own arguments instead.
6. Be willing to walk. You can tell in the first five minutes if they really want to sell you a car or not. I've sat there for an hour with a dealer who really wanted to come to a deal, and I've walked almost instantly with a "take or leave it" type. And do NOT ever go over the final number you had in mind. I've walked over a $250 difference (and ended up saving $1500 by going to a different dealer).
7. Be willing to wait. They'll try to wear you down with mind games, in hopes that you'll either cave or leave. As long as they're still throwing numbers out there, you still have a chance to get to where you want to be.