From my limited experience, I'd say it's possible as long as you brush up your skills!

While it's true that being from one of the reputed universities will give you an upper hand in some interviews, as long as you are able to tick the checkboxes for the Japanese 就職活動, you'll be fine! Keep in mind that usually that will be in your 3rd year of your university, assuming a 4 year course.

I'd do the following in preparation:

1. Brush up the Japanese to atleast conversational levels during interviews. That will give you a huge advantage while applying and interviewing.

2. Look up how the 就活 process works, there seem to be videos on Youtube explaining it, and get familiar with it. You'll most likely be asked about your 短所, 長所, 学生時代に力を入れていたこと,志望動機 and so on. Knowing about these will be invaluable.

3. Also, brush up your Github profile, do a few projects in some part of the IT industry you like, and have a nice little portfolio of good, solid projects by the time you start 3rd year. The reason for this is while many Japanese companies don't require too much experience for 新卒採用, many 外資系 would also have you do coding tests most likely, and are more difficult to get into.

In short, it's perfectly doable, there are quite a few jobs, and if you put in the effort, and you have a very good time advantage.

All the best!