Typically lenders want to see a 2yr work history, whether before or after graduation is not the issue. The also typically want two years of rental history. By the way, again "typically" those years do not have to be contiguous, but they do prefer they be in the same type of occupation. So for example, if you worked in a shoe store your freshman through junior years in college 3 months each year, then in your senior year worked for a fitness center selling memberships... you would have the needed 2yrs of work experience in the same occupation. The same approach is typically taken for documenting 2yrs of rental history.
Notice however that I say "typically" because for every rule there is an exception. I dare say if you could put 35% down and had $1mil from an inheritance in the bank some underwriters for loan programs typically with slightly higher rates, designed & targeted for exceptional situations would find a way to loan you the $$$'s but in such a way as to protect themselves.
The best advise I can give you is make sure you not build a strong relationship have a Smart, Trustworthy and Caring Realtor, but also a lender. As in every industry, the skills, experience & ethics of Realtors & Lenders varies widely and you have your masters that fall into the top 5% of their trade and then you have the majority who do not possess the same skills, etc.. A top 5% Realtor will know who the best Lenders are. One of the key criteria in my book for a great lender is NO SURPRISES, they know the guidelines for loans and understand what the latest requirements are, they find out EARLY on in the purchase process what the home you are interested in has as obstacles to funding and how to work around &/or resolve them.
If you would like to connect with one of my time tested and "battle" proven lenders that I recommend to my client, email or call me!