Bear with me, this is going to "go the long-way round" to get to the point. I'm using Los Angeles as the sample city, as it's somewhat typical for California (and noting that Calif is worlds better than some states in the USA). And warning that some of my info may be a little out of date.
Assuming you can FIND a full-time job, and using the Federal Minimum Wage you'll take home just a smidge over $260 a week as a Head of Household with one dependent. The current California minimum wage for a small business employee is $10.50 an hour. You'll take home about $375 a week, so a 4-week month average of about $1,500. Note that if you are not able to work due to your or a family member's illness, unless you are fortunate enough to have a job that offers paid sick leave, you will lose the pay for the time you are not at work. Miss too many days and you may lose the job.
Transportation - Los Angeles has some public transportation, but not every city has even basic public transportation. A transportation pass in LA is about $90 a month - you'd be hard-pressed to own a car in SoCal on minimum wage (unless you use it to sleep in). Plan on spending several hours of your day on public transportation getting from where you live to where you work. Your choice of employment is restricted by your ability to get to and from it.
You can theoretically get State funding for childcare (now-days) in California up to the point of your earning about $4K a month. So at the $1,500 a month income rate, your childcare for the one child
should cost you nothing. I am assuming that the problem remains that you still have to find a provider willing to accept the rate that the State pays. The going rate for childcare for infants is +/- $14K a year, and older children would be slightly less, on the open market. The State will cover $232.26 a week for an infant (+/- $1,000 a month, which is a huge improvement from when the Daughter was a baby). However,unless you do find a highly-coveted state-subsidized slot, you're looking to spend about 2/3rds to 3/4ths of your monthly income paying for childcare so that you can work enough hours to pay for it.
It's quite common for landlords to demand that you earn 3 times the monthly rent before they'll consider your application. So, hypothetically, at $1,500 a month income you could get a $500 a month apartment. Except you can't even get a parking space for $500 a month. Section 8, while well-intentioned, is a joke. I don't think it's changed much since the Daughter was a child, but back then there was a 3 year waiting list to get a Section 8 voucher. And then you would find that landlords wouldn't accept them as they could earn substantially more renting on the open market. The places that would accept Section 8 were not anywhere you'd want to raise kids.... You may be able to find a one-room place with your budget, possibly, but again, it's going to be in a neighborhood you don't go out after dark in. Unless you have a death wish. Then again, the drive-by bullets will get you through the stucco walls of the place while you're sleeping, anyway.
And finally down to Medicaid (in California called Medi-Cal). Your expenses in an emergency room are covered for emergency care to stabilize you. Once you are stabilized, unless Medi-cal will cover the cost of inpatient care, you're out on the street in your hospital gown until you are sick enough to need emergency care to be stabilized again. And the hospitals do biopsy your wallet before you are seen by anyone. Assuming you have an address, you will be assigned to a community doctor that Medi-cal will reimburse on a "per head of case-load" basis. They have quiet a case-load: the waitlists are obscene. Medicine is restricted to a formulary of approved drugs for specific illnesses.
[Extended Ramble: I remember that the Daughter used to get horrible ear/UR infections almost constantly. The approved treatment is Amoxycillin. It didn't work. But every time (we're talking every other month) she had an ear infection we'd have to do a course of Amoxycillin before they'd move to the next drug
even though her records showed that it was ineffective. In time, that one didn't work either, but then we'd have to go through the first two to get to the last one, that did clear the infection up. Except that the course of treatment was for, I think, 10 days, and it wasn't long enough, so the infection came back.... and back to Amoxycillin again. Which was better than in Texas, where you were allowed three prescriptions per month. Period. If you could get them. I remember bringing the Daughter home from the Emergency Room at 1:00am and stopping in the only local 24-hour pharmacy to pick up a prescription, only to have the Pharmacist tell us he wasn't going to fill it because the State paid him less for the medication she desperately needed than he paid for it. He threw the prescription at me - literally - while muttering something unrepeatable about "welfare scum" and told me to get out of his store when I asked if he could phone the hospital to see if they could substitute something else. {I was in graduate school on a scholarship at the time and had her with me at the counter.} I had to go back to the ER, to find the doctor who had seen the Daughter was no longer on duty and wait hours to see another one. The Daughter had an extremely high fever ... it was not a good day for us. But Texas was like that, generally. We were happy when we could leave it behind.]
But that's neither here nor there, for this post. Other than to underline that if a child is ill, it can't be left in daycare and you can't work if you don't have somewhere to leave your child where they will be cared for. I was fortunate in that I was going to University, so if I had to miss class I could manage well-enough by reading, getting class notes from friends, and doing extra work. (One semester I lost 6 full weeks of classes out of an 18 week term, due to the Daughter being sick. I could not have held a full-time job - I'd have been fired for absenteeism.) I did have part-time jobs, in addition to being a full-time student, for my entire academic career, but was fortunate in that they were extremely flexible as to the hours I was on-site. That is not a common thing to find in an employer.
In time, and we're talking like the better part of a decade here, I was able to get a job with good health benefits, sick pay, and a pension. It didn't pay well, but just enough to keep us afloat and those benefits were gold. I was able to build on that and hop up from job to job. It was only a few years before I retired that I was able to be only working one job - I always had a couple of part-time or contract jobs on the side.
So, I managed to get my kid raised. That was ONLY possible because I bypassed the childcare hurdle by taking out a huge student loan debt to pay for private childcare for all those years. [I'll be paying on it until I drop dead, but it's been a good investment.] And because, when I re-entered the labor market
my employer offered a decent, affordable private medical insurance. If we'd been on Medi-Cal, I could not have done it and heaven only knows how our lives would have turned out. [I've seen that play out for others and lived with it as a recurring nightmare for a very long time.]
I don't know what Medicaid is like in states like Texas now. And I don't want to look. Back then, Texas had a highly-fragmented patchwork of several dozen different programs, each with different eligibility criteria and benefits. In both California and Texas there were no programs for adults who were not seriously disabled and on a federal program (SSI/Medicare). But the fact then is the same as it is now - if you are ill, or responsible for an ill family member, you cannot be at work. Obamacare gave states the option to expand Medicaid to cover all adults. Medicaid is an awful program, but it is better than nothing at all. Because if you have nothing at all and you or your kid is sick, you cannot work. In the USA, everything hinges on that. If you get bumped off that treadmill, it's difficult to not go into a spiral down that you don't even want to imagine - and that is incredibly difficult to escape. Honestly, it's your worst nightmare.
If they don't sort it out (medical care, childcare, affordable housing), eventually I really do believe the economic system will collapse. And even more people will end up in misery than are already there now.
References:
https://en.wikipedia.org/wiki/Minimum_wage_in_the_United_Stateshttp://abc7.com/business/minimum-wage-increases-by-50-cents-in-california/2849697/https://work.qz.com/1264246/daycare-costs-how-much-us-families-spend-on-childcare/https://www.ccrcca.org/providers/subsidized-child-care-providershttp://dpss.lacounty.gov/wps/portal/dpss/main/programs-and-services/calworks/https://www.cde.ca.gov/sp/cd/ci/mb1708.asphttp://www2.cde.ca.gov/familyfee/famfeecalc.aspxhttp://www.sacbee.com/site-services/databases/article145228629.htmlhttp://seiu99.org/2017/11/14/moving-forward-new-child-care-pay-rate-increases-in-2018/https://la.curbed.com/2017/12/18/16792996/los-angeles-rental-prices-map-2017