Monthly Rent : 3300 ( east bay 45 minute train ride into SF)
Utlities : 350
BART riding : 260
BART parking : 60-100
or Drive to SF and Car parking $500 ( instead of the 360 BART )
Groceries : 1400 ( 2 teenage boys eat )
Car payments + insurance : 800 ( 2 cars )
renters insurance : 120
Clothing : 300 ( teenagers outgrow stuff fast )
Cell phones : 300
6930 so far... no savings, vacations, entertainment or misc taken out
4670/4 = 1167 per person a month / 4 is 291 a week per person left for savings vacation misc and entertainment
1 family outing in the bay will run $300 to $ 500 easily
BTW to buy a house you typically had to come in with an offer 10-25% over ask and typically a full cash offer would get the house. Good luck buying a house with a mortgage ( the house across the street, in the east bay, went for 699k and it was only 900 sq ft )
But it's also true that if you're starting with nothing, saving for a down payment in such a housing market is unattainable.
Life is different when you arent single
Living paycheck-to-paycheck means if you miss one paycheck, you'll have bills you can't pay. With the numbers you've provided, I don't see how your income and essentials would force you to not have savings to cover a few months. You didn't mention how many income sources your household has; even if 75% is from one source, having a second source does add a lot of security.
I'm a Midwest non-tech worker. I live in one of the 5 largest cities in my state. It's very foreign to me that such a large income wouldn't allow you to feel financially secure.
A starting engineering salary in the area is ~65,000. 1, 2, and 3 bedroom apartments in my complex are $830, $1200, and $1500 respectively. I'm ~2.5 miles from work (7 minute commute via car) and <0.5 miles from a grocery store. Houses in the area with a really good school system are 200-400k typically.