I have vast experience in MSSQL to MYSQL migration, and have till date migrated more than 300+ MSSQL database to MYSQL. I have around 8+ years of SQL development, .NET and database administration experience and have around 4+ years of MYSQL experience working in all newer to older version from Mysql 5.5 to 8.0, +2 years experience in AWS cloud (RDS databases , EC2 instance database and complete cloud based solutions)
Experience in end to end migration which involves complete schema migrations (view, function, stored procedures) and complete data.
I have developed my own tools to migrate data from MSSQL to MYSQL and vice versa, and have also developed first ever MYSQL to MSSQL replication tools which is heavily and widely used in companies.
Based on project description seems MSSQL need to be migrated to MYSQL without downtime we can achieve this using transactional replication.
Before concluding need to understand existing system and exact requirement which will help to achieve assigned project.
To add more : I work with specialised team which are experts in MYSQL and MSSQL and have completed tons of migrations.