Well you're right. Getting started with Bitcoin as soon as possible is a good idea and using DCA method can help one to be accumulate assets as the time goes on. As having discretionary fund is good to help one when investing but it's good to consider the idea of also having funds that can be use to sort out other financial problems, so that you won't forced to touch your investment money when time is not right yet.
And this step, will also help one to make well plan decision and avoid mistakes that might ruin their goals.
Though, there are some cases where the individuals don't really care to have a plan about keeping funds aside to be used for other financial obligations. All they want is to build up their investment and emergency fund at the same time, not minding how stressful it would be, which might also be some risks too.
Which is why it's important for one to balance both investment and other financial obligations.
It is never a good idea to wait to invest if you have a source of discretionary income. However, if you create some other type of fund before creating an emergency fund, it will never be the right move. Because first of all, you have to protect your holdings and then you will have to create other funds depending on your financial situation.
If someone does not have an emergency fund before starting investing, then that person can create an emergency fund along with investing if he wants. If you stop your investments to create an emergency fund, then it will never be the right move. You have to move forward with all the aspects. Investing and emergency fund at the same time will not be very stressful.Because if you have $50 to invest, you can invest with $25 and create an emergency fund with $25. If you move forward in this way, it will not be very stressful for you.