If you were to borrow under the 7(a) Express loan program, it might be structured as a $200 thousand term loan and a $150 thousand revolving line of credit. How much you would have to "invest" to get the line of credit depends upon the lender. It will depend upon how creative the lender decides to be.
How did you reach the conclusion that you need $150 thousand for working capital? Seems like a lot for a cafe. Is this based upon a cash flow projection or are you just trying to get a reserve for 3-6 months of expenses?