I need to be in the US for 10 days to ask for a SSN
You'll get it faster if you wait a bit because of the delay in updates between CBP/USCIS/SSA, but technically you can apply for it on the day you land.
I need a SSN to build credit
You need SSN for a lot of things, including tax reporting. Your employer may not be able to pay you salary (if you're paid in the US) until you have it, because they won't have a TIN to report your withholdings. But yes, it is also used as an id for credit reporting.
I could build credit by either financing a car with an awful interest rate or asking for a secured credit card.
Yes. Financing a car can be a car loan or a car lease. Secured credit card would generally require you to put you a collateral with the bank.
If you have an American Express in your home country, you can also try their "Global Transfer" program.
Your employer may also have agreements with some banks/credit unions which can help you get credit cards (even unsecured) based on your job offer/salary in lieu of credit.
Chase and other big banks do not issue secured credit cards
Really? I don't know about Chase, but others definitely do. Try Wells Fargo, CapitalOne, Discover, Citi, Bank of America - just to name a few.
Opening a US bank account with my passport alone will not help me build credit.
Bank account doesn't provide you credit, so it doesn't get reported (to credit scoring agencies, it is reported to a different system).
My initial concern is about having proper credit history to buy a car and not have to rent a car for months, which is a huge sunk cost.
It would take about a year to build an initial reasonable credit profile. I'd suggest buying a used car instead of renting/leasing, as a more cost-effective measure.