COE+Visa = How long?

Hello, and thank you in advance for answering my question. I was recently offered a job by a company in Japan. They would like me to start work at the beginning of April. Tomorrow, I plan to send the necessary documents for the company to apply for a Certificate of Eligibility on my behalf. From there, I understand I have to wait for the company to receive and then mail me the Certificate of Eligibility, and from there I have to take the COE to the Japanese Consulate in my home country and apply for a visa before I can start work in Japan. In your experience, how long does this take? Is it possible for all this to happen in time for me to start work in Japan at the beginning of April? Is there any way that you know of to speed up the process? Or, is there a way for me to work in Japan while waiting for my visa to be processed? Thank you for your replies, and I am sorry if this question has been asked before!

CEO usually takes 2-6 weeks (but can also be 1 day or 3 months). The actual visa usually takes 5-10 days (but can also be faster - seldomly slower).