No, you can put down whatever you expect your income to be and receive subsidies based on that. If you end up making more than you expect that year (good problem to have!) you'll have to repay some or all of the subsidies on your tax return.
You just need a basis for proving your current or expected income.
Also, in CA, you can make an "urgent" application and be enrolled within 2 days. I requires some pressing medical problem, but that doesn't have to be life or death.
Generally if you want gov assistance in the US, you pretty much need to be poor for a full calendar year, plus about 4 months.