In this project I'm trying to run mysql testcontainer with liquibase migrations in test environment.

You should have docker (I'm using v.20.10.5 for this demo).
Run in bash (convert it to powershell if you're on windows):

 docker container run \
 -d \
 -p 3306:3306 \
 -e MYSQL_USER=user \
 -e MYSQL_DATABASE=first_schema \
 -e MYSQL_PASSWORD=pass \
 -e MYSQL_ROOT_PASSWORD=remote236 \
 --name mysql-demo mysql