Is it feasible to rent a house, mortgage it, pay a down payment in another city and buy another one?
Yes, you can, but if you get a mortgage, you will be in debt. If the debt is too high and it is not proportional to your income, it is also difficult. Income must be 2.2 times the debt, plus your monthly payment. Do the math yourself. There must be a number, and you can't blindly make mortgage loans. After all, the interest on mortgage loans will be much higher than that on mortgages. If you can't buy a house by then, it will be very uneconomical to mortgage the money.