Any successful investment is as a result of availability of a good source of income and emergency funds and emergency funds plays a big role in our Bitcoin investment because without emergency funds our investment won't go anywhere even if there is discretionary, because one will definitely touch his or her investment when it is not mature, emergency funds is the motor that drive our investment to the point we desired or wish and once there is problem with the motor ( emergency funds) our investment will begin to shake and as such emergency funds is something we should joke with while carrying out our Bitcoin investment.
You are doing a mistake somewhere. Emergency funds are typically removed from your discretionary income, same way you remove your investment funds because they are not part of the must monthly expenses to be made. However, it should be prioritized every month as it is a savings plan that lest you cover any unexpected expenses that may arise in the future. So, same way you are taking out money for your investment either through dca or whatever strategy you are using to invest you as well can save up your emergency funds.
Although you don't really need to build your emergency funds before investing you can do altogether whichever way you choose to do it. Building an emergency funds does not stops you from investing with a specific percentage and vice versa.
Discretionary income isn't just for investing only you know? You can as well get your Retirment funds, vacations savings, big purchase savings, emergency funds and investing funds. Its literally the income left from you must monthly expenses.