Newbie here, should I house hack while in grad school (FHA)?

[Christopher Lora]

I live in a HCOL area, NYC metro area, currently in grad school paying $800/mo rent all included, $30/mo cellphone, $70/mo clunker car insurance. No credit card debt at all.

Student loans in deferment ($13k and going up), I can choose to pay student loans as I study, working UberEats making roughly $700-1000/week (just the weekends) but stacking cash in the meantime.

I have 800+ credit score and can gather $20-30k for a downpayment if necessary (not that I can afford much with that in my area) but I have been hesitant of even considering buying a home due to lack of steady income. I don't want to say UberEats is "steady" but it is really consistent, especially if pandemic worsens/more opportunity.

Should I actively seek to find a property I can "afford" now and house hack it considering I'm paying $800/mo in rent to someone else, or should I just be patient and finish my studies and then jump in with a steady income stream?