How would you handle a site migration?

Perhaps this, Importing a database from a custom built CMS to WordPress, and this, Migrating A Website To WordPress Is Easier Than You Think, may provide assistance or some leads?

I had read the second one but not the first one. I am pretty familiar with WordPress but not comfortable enough to import an old database into a wordpress one. Wondering if I could find a company that could just do the import.

Posting jobs is not allowed in theme forums. You can look for a reputable person on https://jobs.wordpress.net/ or https://directory.codepoet.com or https://upwork.com

(FYI, it’s not a good idea to respond to work offers from random forum users who have read about your post.)