At your income level—I would get a cheaper car and keep your savings. 100k savings is a GREAT starting point for nest egg if you invest it correctly. Especially if you plan on letting it grow over decades.
But if a Tesla is non-negotiable, then maybe finance part of the vehicle cost and structure the loan so you can eat the monthly payment without taking a huge hit to the rest of your monthly budget/lifestyle (and most importantly—your savings rate). Cut back on frivolous parts of your life if needed.
I would note that interest rates are climbing rapidly right now, and those rate hikes alone could swing your monthly payment by $100+/mo in worst case. Buyer beware.
