Arksansas - Where it's a crime to not pay rent.

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Just to clear things up.  The lender is looking for an income of 35-45% above the monthly commitment to the loan.  So yes, $16k should be just fine for a $500 a month commitment.  

As for income tax.  A person who earns $16,000 a year pays zero federal income tax.  0-9,700 at 0% then factor in the standard deduction of $12,200 and you'd still pay zero until you earn over $21,900.  State income tax would be roughly $450 a year.  

If you still feel its a little tight, add a roommate in the beginning, people do it all the time there is an extra $300 a month covering 60% of your mortgage.

There more upward mobility in AR than in CA.  Even if the income is lower, the cost of living to income is much more preferable in AR, without the tax liability federal and state that comes with CA.  The great thing about getting into real estate early is you are hedging for inflation, you are really putting money back into your pocket instead of wasting it on rent.  Opportunity costs should really be considered at an early age.  

If repairs are a concern, a home warranty is $38 a month, I use them on properties that have old AC units and old hot water heaters.  Last year my 20-year-old hot water heater went out on a property, the cost was $125 for the deductible.

Your down payment for this property in Arkansas is $18,000, which you can achieve by saving $75 a week for four and a half years.  How many decades will the down payment savings take in CA?  Despite being classified as poor and in poverty by the federal government, you can do just fine at $16,000 a year in Arkansas and will be much better off than someone who lives in CA making $60,000 a year.  

There are also cheaper smaller homes in AR.

The Foreclosure Fear/Myth
What happens if I go into foreclosure.  The bank takes back the house, places it at an auction, sells it at the market cost most of the time, then takes what is owed plus legal costs associated with foreclosure, and the difference must be sent back to the borrower.  So you are most likely even going to get cash back after foreclosure.  Finally, you are no longer the cool kid with a great credit score for a few years, boohoo.

If you make $16,000 a year living in AR, can be disciplined enough to save $75 a week for 4.5 years, buy, buy, buy, buy.