Having a source of income is a crucial first step in bitcoin investment. It does not only allow you to invest regularly, it also helps you hold your bitcoin stash for a long time without premature sales. I don't think that investing when you cannot sustain it would be very advisable since this is the beginning of bitcoin gambling. When a person invests without having what he's doing, he's only monitoring the chart to see that it has appreciated before he withdraws it. Appreciation may happen and depreciation may also happen. This is why long term holding remains the best and as a newbie, long-term holding won't be very possible when you don't have anything that gives you a source of income.
Anyone that doesn't have a source of income has no business investing in Bitcoin because he needs to survive first before thinking of investing, so on that note, what the said fellow needs is a job in other to take care of himself and his basic needs.
If anyone decides to invest in Bitcoin base on the fact that some money gets into his hands without him having a weekly or monthly income that he can get his discretionary income from, it will only be a matter of time before he falls back to his investment just to survive , so it's a terrible idea to go into Bitcoin investment or anything other investment without having a source that can sustain the investment on the longer run, because starting is easy but sustaining your investment is another thing entirely.
Even if you don't have a source of income, you can still invest into bitcoin provided that you have a discretionary income. For instance, I know about bitcoin potentials and don't have a source of income, I can still invest into bitcoin. If I am given funds as a gift which I did not expect, therefore, I have no plans for the money. I can simply use the money to invest into bitcoin and act as if I wasn't given any funds. You must not have a source of income first before you can take advantage of the opportunity to own a little sats than staying in the no coiner level.
However, a stable source of income is important in order for you to keep your bitcoin accumulation ongoing consistently and persistently for 4-10 years and above. Since you have bought your first bitcoin, it shows a sign of commitment because you bought even when you don't have an income. You can look for a means of income with a discretionary income so that you can continue your bitcoin investment.
If I said I don't really agree with what you said about someone without a source of income having a discretionary income then am living to you. Without a source of income I don't think it will be possible for you to even think of investing, investment is not for everyone and as such I have seen someone who is finding it difficult to feed to be talking of having extra cash to invest with. You can talk of not having a stable source of income but not having a source of income at all is the same thing as not having a discretionary income. Just like you said if you are given a gift and decided to invest it in bitcoin, what happened if you are in need or an emergency occurs then you will be forced to fall back to your bitcoin investment. Bitcoin investment is not meant for everyone especially if you can't meet up with your expenses.