This is wrong, it's not a must to keep delaying your accumulation of Bitcoin because you're busy trying to build out your emergency fund which you can build alongside your accumulating Bitcoin. As soon as you're sure of having discretionary income you can start investing into Bitcoin with some parts of it, maybe like 50% of your discretionary income and spread out the second part to building your emergency fund and other variances of backup funds and/or floating cash. The quantity of discretionary income you allocate to buying Bitcoin and building backup funds is at the discretion of the investor.

You can continue investing into Bitcoin and building your backup funds continuously alongside it until your emergency fund can service at least 3 months worth of your expenses and then you can choose to divert the funds used in building your emergency fund into increasing your aggressiveness investing into Bitcoin. Building your emergency funds should not be an excuse for you to delay kick-starting your investment into Bitcoin.