Asking part of the salary in advance while starting a postdoc at a US university
My university would give you a moving allowance that could be used to cover first and last months' rent plus security deposit on an apartment or rental house. You might start with asking what kind of moving allowance or support they offer and whether upfront rental costs like these are covered. This is not considered an advance on salary at my university, but is part of the cost of hiring. The university simply pays it to get good people to come work there.