It depends on what bureau/scoring model the dealership uses and what you are comparing to. I’m assuming you are getting your credit score from FICO or your bank (4 of mine give it free but different scores from different versions/bureaus), that you’ve cleaned up all of your bureaus (no good if Equifax is clean but Transunion is a mass grave), and you’re just asking thresholds?
It depends on brand/region/sometimes dealer. For a lease probably 620-650 for any kind of approval, 720+ for Guaranteed A Tier. Some banks and captives don’t exclusively look at credit score. For instance, I don’t know if this is true today but as recently as a couple years ago if you had a bankruptcy on your credit report no matter how high your credit score was you were an auto-decline in Bank of America. You could have an 800 credit score and $1 million in cash and they would not give you a checking account and a debit card.
Some banks just look exclusively at score although they all should take into account debt/income ratio. Some decline for exclusionary events like my Bk example at BofA. I don’t remember if it’s MB or BMW, but for one of them if you had one of their cars repo’ed, you’re black-listed forever by the captive (fool us once, shame on you). Some lenders are less concerned about late pays and issues with the credit score because of store cards or credit cards or potentially even your mortgage, but if you have an open repossession or a recent repossession on your credit for any bank/brand they won’t give you a loan / lease.
I can totally understand why MB said no and FCA said yes, the latter buys deep. MB would rather make less interest income on markup and employ fewer tow trucks.
And none of this is hard and fast, it depends on the management, the financial environment, etc.