There is no native way to automate this process without utilizing the API.
You’ll have to use either the Scripting Block, or else some external tool like Zapier or Integromat to utilize the API for syncing data from one base to the other.
If you are familiar with Zapier, for instance, you can set up Zapier to watch for new records in a table. When a new record is detected in the table, you can have Zapier create a new record in the target base (the one you want to duplicate into), populating that new record with data from the record that triggered the Zap. I think this is a relatively code-free solution.
Alternatively, if you are capable of writing JavaScript, or have someone who is, you could use the Scripting Block to write a script that, when the script is run, takes some subset of records from the base of origin, packages their data up into JSON, and then sends them to the new base via an API POST request.
I believe that there are some 3rd party services that offer this service or are planning on offering this service soon, probably for a monthly fee. Maybe some of them will chime in.