No, she can't.

The process to amend the constitution of Japan [0]:

1. two thirds of the house

2. two thirds of the senate

3. referendum

LDP just won the house. IF all LDP house representatives agreed with Takaichi then she could pass the first stage. Only two left!

[0]: https://ja.wikipedia.org/wiki/%E6%97%A5%E6%9C%AC%E5%9B%BD%E6...