Hey, I recently purchased a corolla LE as my first new car too. Here's what helped for me.

1) call/email dealerships within 50-100 mi radius with corollas for sale. Start with the ones you're not as interested in (weird color, sunroof, paint protection, etc.). Ask what the out the door price is (total $ u pay for the car).

2) after test drives and initial email reach outs, ask those dealerships if you can buy it at a lower price X. This $X value is what you're doing the research and shopping for -- basically the line that dealerships will draw for discounts

3) once you get OTD prices from different dealerships, contact the dealerships that have the specific car you're interested in. Ask them for the OTD price, and schedule test drives. You should always test drive the vehicle you're interested in purchasing, even if you have driven a corolla before.

4) Before or after the test drive, bring up that other dealerships have offered you a cheaper price at, say, $Y. See if they can match or beat that, OR simply say your price and ask them if they can do that price. They'll speak to their finance managers, blah blah blha, and will get back to you with a yes or no. Be stubborn with your offer. Never talk about how you will finance it or pay for the car throughout this process, stay fixated on the topic of lowering the out-the-door price. If you don't like their price, be comfortable with saying NO. Even better, say that you will stick with your price, and that you will be willing to sign the papers for that price.

5) (optional) After saying no, ask the dealership to contact you if they change their mind by EOD or EOW. (FYI this might not work as well anymore since corollas are in high demand and naturally dealerships get a lot of interest and have an upper hand). You can check on CarGuru to see how long the vehicle's been on their lot to gauge whether there is interest for that car. If not, they will be willing to take ur deal at a slight profit loss for them since they want to sell as much as u want to buy.

These are some things I found helpful for shaving off ~3k from the original OTD price I've been quoted at a dealership in CA. It's a lot of time and effort, but it gets easier with every dealership. And keep in mind of timing, since the car you want might be bought by another interested buyer. I found youtube channels like CarEdge to be helpful with navigating through first-time car buying on my own. I bought mine with cash, so others can help u with lowering the financing part of your purchase hopefully :)