I've spent most of my career in the Bay - $150k in the Bay Area without child expenses in a single-earner household with the following common lifestyle choices will about break even month-to-month while fully funding a 401k (in the "core" Bay Area - SF, the Peninsula, parts of Oakland/Berkley):

Eats out frequently, goes out for drinks occasionally, travels a few times a year, owns a new mid-range car, lives in a modern apartment complex or small home/condo near a downtown area (with a < 30 minute commute). New electronics, big TV, minimal but high quality furniture.

Pairing back on those choices you can begin to save every month, but not at a pace to buy a home in a reasonable time frame.

On dual income assuming consistent earnings YoY you can start to buy a house in a cheaper neighborhood later in life, around the time many are starting to have kids.

I have to imagine kids can put a 5-10 year delay on buying a house without various kinds of assistance.