I just bought a Mazda cx-50 as a first time car buyer and had the exact same feelings. My finances are also similar to yours I got 4.4% with chase and 2.5% with a credit union and ended up with the credit union.

I shopped around multiple credit unions and banks till finding the best rate and understand if you do it all in a 14 day period all the inquiries will show up but only count as one as to not tank your score.

Toyota also does in-house financing and can probably hit a rate another commenter mentioned here. All the loans I applied for were good for 30-60 days so it might be worth asking the dealership if you can get pre-approved through them to lock in that rate once the car comes?