If you are guaranteed of discretionary income, there's no need for you to build an emergency funds first; you can start your investment right away. Then after you have spent 1-2 months accumulating Bitcoin, you can start building your emergency funds gradually so if you have any emergency, you can freely sort it out.
It is never a good idea to create an emergency fund after investing or after 2 months or 1 month. You have started investing today, you can set aside money for an emergency fund from today, it will be good for you. Because if you want to create an emergency fund after 2 months, then if you face a financial crisis during these 2 months, how will you deal with the financial crisis? So, creating an emergency fund along with investing is a wise thing to do.
If someone buys Bitcoin with a loan, it means that he does not have an emergency fund and reserve fund. If he buys it when the price is lower than expected and later sees the price of Bitcoin falling further, then he will be in a very bad state mentally and if at that time his income source is closed, then first of all he will not be able to buy Bitcoin anymore and will have more difficulty in meeting his daily expenses. At that time, if he has a loan and has to pay only the monthly installments, he will be in a completely devastated state and will be forced to sell Bitcoin at a lower price than expected.
A person can invest by taking a loan, there is no problem in it. But before a person takes a loan, he should check whether he can repay the loan or not. If a person has the ability to repay the loan, then he can invest by taking a loan. If a person does not have the money and if he is willing to invest with an emergency fund or reserve fund, then this will never be the right decision for him. Taking a loan does not mean that he does not have an emergency fund or reserve fund.