The median price of American homes is $400k. In California it's $860k. In the Bay Area it's $1.5MM. You can get a house in the Bay Area for under $1.8MM, but you need a $360k down payment, and you will likely face a tradeoff between good schools, safe neighborhoods, being within walking distance of anything, and having a nice sized house. Outside of NYC, these numbers are the upper echelon. If you disagree, you have very expensive taste masquerading as requirements.
On that point about home sizes, Americans are frequently surprised how much less space Europeans are fine living in.