There are several things that you are not able to do in Japan without a Japanese Telephone number.
I found that having a Japanese number was necessary to open a Bank Account here in Japan as well as Rent an Apartment here in Japan. I found it relatively easy.
I think there are many options, but I chose the option to buy a phone and obtain cell service from a provider that provided me with a SIM card that I was able to insert into the phone.
I bought my Phone from Amazon. It was previously used but fairly inexpensive, and when I got it, it looked brand new, so I was very happy with it. The process was pretty easy.
Most difficult was navigating through the process of not understanding Japanese and having to use Google Translate to convert everything into English. It took a little time but it’s done now.