You don't need to have a stable source of income before investing but somehow along the line, the stable income is still needed to maintain the steady cash flow that will continuously make you to accumulate more bitcoins because even as you invest within your discretionary income, if there is no steady cash flow it means your DCA will not be regular thereby it will try stagnate your accumulation process and the need to also have a stable income is so that you can remove the fear of market actions such as volatility but when you don't have a stable income source, at any slight changes in the market you will already start to shiver because it will look as if you don't have any back-up funds to ginger your morale during the time of constant market fluctuations.
You are right to highlight importance of stable income when investing in Bitcoin even if you can start with what you have. Regular income is good for two main reasons first of all it will consistently gives you chance to invest over time and continue your DCA which steadily grow your Bitcoin savings and give chance to buy more when prices are low. Second stable income gives you peace of mind during Bitcoin wild price swings. When you have money coming in means you will not get panic and sell when market drops so this will stick to your long term investment plan and reach your goals without as much stress.
Stable source of income is important but beyond it we have to consider the basic expenses of an investor, if his expenses is beyond the income then there'll be a problem for Bitcoin accumulation. But if the investor can somehow cutdown on his expenses he might have some money to put into his discretionary funds from where he can remove the percentage to buy Bitcoin. So the equation should be income - basic expenses = discretionary funds. If income is constant that means that basic expenses is where an investor can make adjustments to be able bring out discretionary funds.
If basic expenses like food and rent is taking up all the stable income and he cannot adjust it to squeeze out discretionary funds that means that Bitcoin accumulation will have to be suspended for the time being. Total income and basic expenses are the determinants of discretionary funds, if you get it right you can do DCA method for years without stopping. Another important thing to note if you want your DCA method to last is to always try to increase your income. Get a better job, learn a skill and find a side hustle, try every legal means to make more money so that you won't struggle to get discretionary funds. That is where DCA funds comes from.