Of course, it is important to know when one has an emergency before saving Bitcoin. This should be at least 6-7 months of his necessary expenses in the emergency fund. Yes, you are right, he can save some amount of Bitcoin every month until he accumulates his emergency fund. Which he will gradually accumulate his emergency fund and start saving Bitcoin with it.
There is no guarantee that an emergency will not come, when he invests some amount of money in Bitcoin, if at that time he needs money in an emergency, he can spend the money in his emergency fund, which will not put any pressure on his Bitcoin investment.
You will only allocate emergency funds for Bitcoin investment, despite having an emergency fund, you will have to increase your source of income. If you are in a working situation, you can work hard to earn more money so that you can add more money to your investment every week, but there are some other ways that you can follow to help you increase your money and if you have bad habits, you can abandon them. Because bad habits only waste money, that's why I say abandon bad habits because you can save some money from there and connect it to Bitcoin investment.
It will only depend on you how to increase your Bitcoin investment, these strategies must be known and saved for a long time, so it is most important to have a plan. Remember that nothing reaches its destination without a plan.