@HansHeintz Dataverse tables can be defined in a "Solution".
The "ignorance" of using a Default Solution initially doesn't matter much. You can create a new solution anytime containing any combination of specific Components from your Default Solution. Sure, you'll need to go through and separate them out from other things that may not be needed to be in the Solution at all, but I presume this shouldn't be too hard in most cases. In your case all you need to do is add the Tables you need to a New Solution - you can add them directly from the Default Solution into the New Solution and even pick which specific Tables you want.
Since you have a Default Solution, you can create a New Solution - from the new Solution, you can "Add Existing Components" - this can be all the Tables your App needs. For simplicity just say "All Fields" for the Tables you need. You can export only certain Fields but for simplicity let's just say that for each Table you need everything from that Table, All Fields, everything. When adding a whole Table it is pretty easy to specify to "Add All Assets" from that Table. However, you only would add the Tables from the Default Solution that your app needs and not necessarily all of the tables and not necessarily all of the components from Default Solution.
Then, add the App to the Default Solution.
Then, Export and Import the Solution and this should be easier.
If the Import ever complains of Dependency (usually does not happen though) you can try and carefully go to the Solution, add any more dependencies, try Export/Import again in that rare case it happens. I do not have this happen usually though on anything that mostly purely Dataverse.
If only Tables are needed, it should not be too complicated to do, and should not need the involvement of a 3rd party because this is something that can be done in simple way out of the box and no need to move each table manually or create Tables manually in target environment at any time in general.
For now, I presume you do not need to do something more complex like copy Specific Records from Dataverse Tables that must be present in the target environment too right away in the beginning (for this, I might use something like Dataverse Configuration Migration tool https://docs.microsoft.com/en-us/power-platform/alm/configure-and-deploy-tools which is a Microsoft tool, not a 3rd party tool) or to do something even more complicated and specific than that when initializing the target environment (for that I would use Package Deployer https://docs.microsoft.com/en-us/power-platform/alm/package-deployer-tool another Microsoft tool). The use of these tools is advanced and I won't go into them for now. I presume you do not need these for now and you only want the Tables and not the Records inside those Tables or much less anything even beyond that.