If you are willing to spend some money, there are several tools that various companies put out that convert entire Access databases to other formats, like SQLite, that ArcGIS Pro can read. I am not aware of any free or open-source tools that do entire DB migration.
If there aren't too many tables, then you could export tables as CSV or to Excel worksheets and then open them in Pro that way. If there are a lot of tables, you could script something similar.
One other idea, although convoluted, would be to convert an ACCDB to MDB and then use ArcGIS Desktop/ArcMap to convert/copy from MDB to FGDB.