People's income and expenditure are not fixed. Some people have much less expenditure than their income and some have much more expenditure than their income. However, normally those who have a discreet source of income may have an expenditure of 70-80 percent of their total income. The money left after expenditure is basically discreet money which is needed for investment.
Now, there is no need to deposit this discreet money in the emergency fund at the beginning, especially for investment. Because your investment fund has not become valuable yet. So there is no need to pay much attention to the emergency fund at the beginning, rather you try to pay attention to investment at the beginning. Emergency fund becomes important for you after starting investment. If your discreet income is very high, then you can also focus on building an emergency fund along with investment. Remember, there is not much need to buy rope before buying a cow. So delaying investment to build an emergency fund will not be the right thing to do.
I see where you are coming from, but I think it depends on the individual situation. Starting investment early is definitely smart because time in the market matters a lot, but at the same time, not having any emergency fund at all is sha risky.. Life is unpredictable, and if something urgent happens, you might be forced to sell your investment at the wrong time just to cover expenses.. That could easily wipe out the progress you have made.
I believe both can go hand in hand, even if it is small. You don’t need a huge emergency fund before you start investing, but at least having a little cushion can give peace of mind and protect your Bitcoin from being touched when life bring surprises. The rope and cow example makes sense, but if the cow runs away before you get the rope, you are left with nothing. Balance is always the key..
It will never be a good decision for you to delay investing to create an emergency fund because you can miss out on many buying opportunities during the time you wait to invest to create an emergency fund. It will be better if you create an emergency fund along with investing.
As you said, what will happen if your cow runs away before you get the rope. That is why you need to create an emergency fund along with investing. For example, if you have $150, you can invest with $100 and create an emergency fund with $50. If you go ahead like this, it will not take you back from the goal of building your portfolio and you will not miss out on buying opportunities. If you have any kind of unexpected financial disaster at that time, you will be able to deal with it. Creating an emergency fund along with investing will be the smartest thing to do.