Balancing your financial security is a good thing while investing in Bitcoin because investing in any business whether in crypto or any other business without giving much attention to saving is no a good practice as it will affect your financial stability and emergency fund should be as a matter of fact be compulsory for any individual who is ready to investing in Bitcoin because there are other things that will also need finance so putting all your money inyo Bitcoin accumulation will be harmful because Bitcoin investment is focused on a long term basis
If you focus on one thing, then your other side may suffer. You have to balance all the aspects. For example, along with investing, you can create an emergency fund. If you want to invest $5 and if you don't have an emergency fund, then you can keep $2 for the emergency fund and invest with $3. When your emergency fund is fully formed, you can invest the entire amount that you have allocated for investment. In this way, you have to maintain all your aspects properly. If you stop investing and start creating an emergency fund, then it will not be the right decision at all, you have to keep all the aspects in order.
When you start Bitcoin as a beginner, you don't have to worry so much about your emergency fund with long-term investment goals because you are just starting out in Bitcoin investment. You can use the time ahead to build an emergency fund, for example, if your discretionary income is not in a good state (relatively small amount) then you should start saving as much as you feel comfortable with for Bitcoin accumulation. Starting Bitcoin at the beginning may be more fair for your financial situation than building your balance. It is not clear what you actually mean by having a full emergency fund. I think the amount of emergency fund should be enough to meet the daily needs of your family for three months or six months or a year or two years, depending on your financial situation, but if we calculate at a minimum having an emergency fund of three to six months makes more sense to me.