Investing in bitcoin requires that you should have a stable source of income that makes provision for discretionary funds after all necessities have been taken care of, anyone without a source of income should not invest in bitcoin untill the they have secured a good source of income, this is because without money you can't invest and you don't just plug money from trees, you need to work for it, some work harder than most depending on the job/business, and your income has to be high enough to yield discretionary funds before you invest, because you should never invest with the money meant for paying tax and footing your bills, and also while investing in bitcoin with your discretionary funds, a percentage of your discretionary funds should be saved up for emergency purposes so you don't end up selling your bitcoin when you run into a financial crisis and are in dire need of money.
There is no need to create an emergency fund before investing. Because if you are not investing, then in my opinion, an emergency fund is of little importance. Invest first and then gradually build an emergency fund. Or if you have the money to create an emergency fund, then immediately create it as soon as you invest. Try to keep 3 times your disposable income in an emergency fund.
If you think that there is no need to have an emergency fund before investing, then it may not be fair because if you have that amount of funds then you can do it from the beginning. Having an emergency fund from the initial stage of investment will strengthen your confidence in long-term investment. If you do not have the financial capacity, it may be a good decision to do it gradually as recommended by you.
In my opinion, there is a need for an emergency fund in any reality. For long-term Bitcoin investment and for holding decently in each cycle according to your ability a backup fund is of immense importance.
For regular investment each source of emergency fund and floating cash should be expected from discretionary income so it is necessary to formulate a strategy to strengthen the sources of income. It is more important to have a backup fund as well as a floating cash flow to increase the holding of Bitcoin comparatively more. Determining the amount of emergency fund depends on your financial capacity. But there should be money equivalent to at least six months of family maintenance. It should be much better to keep emergency fund for long term Bitcoin Investment above six month.