I dont agree with you. You should definitely have an emergency fund for unexpected events that may happen. If not, you are just going to take your investment later on to attend to the emergency. A 2-6 months emergencies is enough to start an investment you dont need to gather all the money in the world. The reason for having emergency funds is to play it safe while you are starting your investment. There is no certainty of any bad happening but what if? That is the question you should be asking yourself. Because we dont know the future so to avoid any investment mistake why not have an emergency fund. After 2 months you can start your investment but still have it in mind that if you are not satisfied with the amount you have in your emergency fund you can put more funds there.
For the initial stage I think there is no need to think about managing emergency funds because we need to adapt to ourselves in running investments. If we are able to adjust well I think the next step is of course we will get used to thinking about better strategies in perfecting the investments we make.
I used to be like that investing in the early stages I didn't think about making a plan to manage emergency funds because I focused more on buying regularly every week. The journey lasted almost 8 months and in the end I found many correct investment methods that Mr. JJG often said in this thread.