Try searching Ancestry.com for surname Mlynarz, and put Warsaw in the keyword field. There are many interesting hits. Some are passenger arrivals to The U.S., both decades before WW11 and also in the 1930's. Some are U.S. naturalization records (some appear to have changed their name to Miller.)
If your parent's immediate family is not found than perhaps you will find siblings of your grandparents that emigrated earlier in time or right before WW11.
Public libraries that offer free access to Ancestry have been offering that access from home computers since Covid. Check you library's website to see if they offer this.
Another great resource for a multitude of databases.
Old digitized city directories for Eastern Europe and other locations can be searched at:
JewishGen has many excellent databases to search:
You can search old digitized newspapers from around the world. A listing of newspapers available to search on-line (by geographic region):
Hope this helps,