Is it possible to enter Japan with my family?

I'm going follow a Masters' degree in Japan. I have received the COE. Initially plan was to enter Japan in
April,2020.

I have a 1 year and 10 months old kid who need to kept with my own responsibility. Generally to obtain dependent visa takes few months. Therefore I obtained temporary visa for my kid until I obtain the dependent visa. But due to the COVID 19 outbreak all visa suspended.

Now embassy has started to issue the student visa and still not temporary visa.

Is there any way for me to take my family with me before getting dependent visa?

I recommend speaking to your local Japanese embassy - they can give you the official answer, rather than speculation on an internet forum.

also, you need to find a person who takes care of your child, when you are in school.
generally speaking, they don't take care of such kind of matters, when you are a Japanese. but, since you don't know the system in Japan, it is better to consult the administrative staff (or your professor) in the university.
this is more important than the visa.

Almost all international residents in Japan are eligible to bring their family to Japan as Dependents. As long as your Residence Status is in the list below, you'll be able to apply.
https://kohiclicktest.wixsite.com/blog
https://dailygram.com/index.php/blog/769225/jitter-click-test

not applicable for all family members.

Dear Samanthika

Congrats on your selection to pursue the Masters course in Japan.
I was also in your state and I know a few Sri Lankan families who faced the similar situation.

IMO there are 2 options available for you
1. Kindly ask your University to apply for a CoE on your behalf to your child. It may take a while but it will able you two to travel together
2. Japanese borders are opening for foreigners gradually. If the Visa center is offering Tourist visa for 3 months apply for it (kindly ask your supervisor if he/she can be the guarantor) and bring your kid to Japan. You might be able to change the visa type after arriving here and settling down in a couple of weeks.

Make sure you do everything according to the guidance given by your University/Supervisor since you have to rely on everything on them as their student.

All the best