You are absolutely right that it is important to have an emergency fund so that we do not have to sell Bitcoin at a difficult moment and of course we must have an emergency fund before investing.
Having an emergency funds before starting your Bitcoin investment is not a most and don't mislead newbies to be on the waiting side when delay is dangerous.
There's no need waiting to set up an emergency funds of at least three months of your monthly expenses when it will take you 1-2 years to set it up. Will you continue waiting and be piling up fiat that depreciates in value overtime without any bitcoin investment running. Your emergency funds is a backup funds to your bitcoin investment and what are you backing up when you don't have a bitcoin investment.
Emergency funds should be set up before investing by a new investor who does not have an extra funds available that can serve as his emergency funds. Rather, you should start your bitcoin investment with your discretionary income and set up your emergency funds of at least three months of your monthly expenses simultaneously with your bitcoin investment.
You can share your discretionary income to two parts, use one for your regular DCA and use the other part to build your emergency funds. When that's achieved, you can channel the money to set up a reserve funds and when that is also achieved, you can start investing aggressively by channeling that funds to your weekly DCA amount to increase it.