if you can keep an $100 every week for a period of five weeks as a strategy you are adapting to build your emergency fund, then you can as well invest that directly into bitcoin as a way of getting your initial bitcoin stack that gives you an head start in your investment. setting up an emergency fund is important but it is not more important than doing the real thing of building up your investment.

it is just like when one is trying to learn so much even when he is not investing at all, that in itself is another form of time wastage because you will end up starting much late because of too much wastage of time. if you even have a means of sorting out your emergency situation without actually setting up a fixed budget somewhere, there might not be a need to keep some money somewhere sitting idle as an emergency fund. say you are a business person for instance that has fluidity of cash from your business, there might not be a need to keep some money somewhere for an emergency since your business can save you in such time. all you likely need might just be to continue building your stack while ensuring that the business can sort out every other needs including an emergency need.
most of the investors that sells when they are in tight situations likely went in too aggressively hoping for fast returns without setting up good systems on ground and when an emergency comes up, they discover that the only place to fall back to is to offset part of their asset as a means of solving those needs. as long as life is concerned, emergency must always come, the only thing that shields us at such time is when we have made adiquate provision for it.