Rental application question [MN]

I’m not sure if this is the right place to post this. If not, please let me know where to post this.

Hi, so I recently finished grad school in May and I did not get a summer job. I had the luxury of being able to live off of my scholarship money to finish paying my current lease. With my lease ending this month, I applied for a new apartment. The move-in date was supposed to be for this upcoming Monday (7/27), but with the timing of things that obviously won’t be happening.

So while I don’t have a history of consistent income for the past three months (I budgeted my lump sum scholarship), I will be starting a job at the end of August. Should my offer letter suffice as enough proof of income?

This property also does not allow a personal guarantor, only a third-party one that they use (The guarantor). But I don’t understand how it works, because I still have to income qualify (which I think defeats the purpose of a guarantor). Should I just ask a sibling to cosign with me? Is there a way for me to negotiate with anyone especially if I will be starting a new job that will easily make more than 2.5x the rent. Things just feel like poor timing since graduating and I’m not sure what to do or if I even have power to do anything.

Please let me know your thoughts or your experience with providing an offer letter. (if it helps my credit is 680 and I have never missed rent in my four years of living outside of my parents home)