Emergency fund is important to have because unexpected things happened unannounced in life there is every need to make provision for it.
In bitcoin investment you can still get started if your emergency fund is not yet ready provided you have your discretionary in place no one should discourage you not to get started because you still find it hard to figure out your emergency fund, you start buying bitcoin with your small discretionary consistently buying with the dca method and figured out your emergency fund gradually along your buying process as months goes by.
Waiting to figure out your emergency fund before getting started when your discretionary income is already available to get you started may kill your dreams having bitcoin portfolio.
the truth is emergency fund and backup fund are very essential when it comes to bitcoin investment, and not only bitcoin investment, even other investments requires you to have emergency fund and backup fund for handling emergencies when they arises. Even if you don't have emergency fund and backup fund yet you can still get started with bitcoin and start investing in bitcoin consistently with your discretionary income that is available using the DCA method. Normally you build your emergency fund and backup fund from discretionary income, now less assume that your discretionary income is not that large to invest in bitcoin at the same building your emergency fund and backup fund, you can start investing in bitcoin with all your discretionary income for like 5 to 6 months, then after 5 to 6 months you can now start dividing your discretionary, one part for investing in bitcoin, another part for emergency fund and another part for back up fund.