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Discretionary Income should be considered first before your emergency fund, it is from your Discretionary that you will use to buy your bitcoin and continue your bitcoin investment, then your emergency fund is to settle your unforseen challenges or problem which would have make you to sell out your bitcoin when it was not your target to sell.
Emergency funds would still be carved out from discretionary income, you make use of a fraction of your discretionary income(a larger fraction though) to invest into Bitcoin and a smaller fraction to build your emergency funds and other variances of backup funds and with consistency, over sometime, you'll be able to build out your emergency fund to service 3 months of your living expenses or more as you wish and then you can channel it's fraction of your discretionary income into your Bitcoin accumulation to increase your aggressiveness subject to when there's a real emergency and it fulfills it's purpose. Then you can go back to rebuilding it again.
It's a wrong advice to say that a low coiner or no coiner should wait for the dip before they buy because you feel that bitcoin price is high.
Waiting entirely for the dip to buy Bitcoin is a lazy man's investment practice for a low-coiner and no-coiner. For me it's lack of seriousness when you should display commitment towards your accumulation journey. Lazy practices brings lazy results and that's why the no-coiner might never have Bitcoin after a long time because they keep speculating and don't take action and a low-coiner continues to make little or no progress in his accumulation journey since he's gambling with Bitcoin at a time he should be investing with commitment and dedication.