It's not necessary you must setup your emergency funds immediately you start your Bitcoin investment,but at least 3 months is an enough time to do it because it's very important.
It's important that you start building your emergency funds immediately you are starting your bitcoin investment and build it simultaneously with your bitcoin investment till your emergency funds have reached up to at least three months of your income. The reason is because when you fail to build your emergency funds in the early stage of your bitcoin investment, an unforeseen circumstance can pop up and you will sell your bitcoin investment because of lack of early preparation of your emergency funds.
Just like you said that, it's after three months of investing that we can start to build your emergency funds, what if in the second month an emergency occurs. This is why we should give more priority to our emergency funds and our bitcoin investment when accumulating bitcoin. You can share your discretionary income into two parts, use one to invest in bitcoin and the other part to build your emergency for at least three months of your income.
The amount will be based on your calculation and the total amount of you income so you will split all of your income in the right allocation.
Besides that, you will not have to use the emergency fund if you are not in the urgent situation that need money. You can keep your emergency fund in the right place while you can focus with your investment.
Part of your discretionary income is what you are to use in build your emergency funds and invest in bitcoin. If you allocate money from your income that's not your discretionary income to build your emergency funds, you will end up using your emergency funds to take care of your needs and any long term bitcoin investor without an emergency funds is only gambling.