Both are possible, it is just that since we have no way to control the events that happen around us, being too aggressive in our investment strategy can be very detrimental, if we find ourselves facing a difficult set of circumstances.
So the safest path is to build your emergency fund and only then begin to invest in bitcoin, however such an approach has an opportunity cost and you may miss buying bitcoin at an attractive price, so I can understand why you may prefer to take a hybrid approach.
Every investor is trying to utilize any slight opportunity they have to bitcoin at a low profit but comparing both emergency fund and bitcoin investment i think both actually have an important role to play and placing them on a scale of preference to determine the most important will be an individual decision since we all have different responsibilities. As you said we don’t have control over natural occurrences so emergency funds are as important as ones investment to prevent one from frequently taking part of your investment to solve unexpected problems.
I agree with your point, it’s safer to build your emergency fund before investing sso you don’t always refer to your investment to solve problems.