There is no need building an emergency funds to protect your bitcoin investment when you don't have any bitcoin because you have nothing to protect. Bitcoin is an investment and you should be thinking on how you can accumulate as many bitcoin as possible overtime, by looking for other mean to increase your income when you have started investing and cut down your expenses in order to enable keep your bitcoin investment ongoing without selling a dime.
It does not really make sense to be over focus on building an emergency fund for Bitcoin when you have not even gotten exposure to it in the first place.. The real first step is to actually start stacking, even if it is with very little.. Too many people overcomplicate it and waste years planning for a perfect moment that never comes, meanwhile the market keeps moving.. Like you said, the smarter move is to prioritize accumulation and then later figure out how to balance that with other parts of your finances.. And that discipline you mentioned about cutting down on expenses, a lot of us ignore that.. The truth is, if you are serious about holding Bitcoin long term, you will need that discipline to hold without selling at every little life expense that comes up…
At the same time, I think there is another layer to it.. While accumulating is the main goal, one also has to be mindful of not stretching too thin financially, because that is usually what pushes people into panic selling their holdings whenever life hits them with an emergency. I kind of see it like walking a thin line, you don’t need a huge emergency fund before you start buying Bitcoin, but having a little buffer for unexpected expenses can save you from making emotional decisions with your coins. That balance is what many fail to see. It is not about waiting years to save before buying Bitcoin, but about structuring your life in such a way that your Bitcoin stash remains untouched while you keep stacking bit by bit..