Well, a key aspect of the migration from an existing traditional org to SFDX is the clear identification of the metadata subset that comprises your specific customizations to the org. You actually don't want to grab the full contents of the org and convert those into an SFDX project. That's an anti-goal. Instead you need to carefully determine which custom objects/fields, classes/triggers/pages/components, layouts, permission sets, etc., you should be managing under source control and only bring those along. In the end you should be able to apply those to any given org and end up with your customizations applied to that org. In fact, as you develop in SFDX scratch orgs, that's exactly what you'll be doing.
You can use IC to do that by creating a connection to the source and using the subscription editor to iteratively "sculpt" a subscription that represents your specific customizations. Once you have that, you can retrieve through that metadata subscription which will include a corresponding package.xml file, and then you can use sfdx force:mdapi:convert to being the migration from MDAPI format to SFDX format.
I've used this successfully several times now against source orgs in which no packaging has ever taken place. There's an up-front investment in the isolation of your specific value-add metadata components, but it's worth it to leave behind all of the cruft that you shouldn't be carrying around with you, e.g., unmodified standard objects/fields, workflows, layouts, etc.
Regards,
Scott