Most efficient way to PUSH data into data warehouse

I think it depends on what exactly you want to push.

Data that's processed and then is at rest in something like SQL database tables? I'd look at Mirroring.

Data at rest, but it's in files? See if you can use Shortcuts.

If it's being transformed or created by a process like logic apps or Databricks, you'd have to weigh the development time in writing the processes to push the data into a Fabric destination against writing it to a destination you have available and using one of the options I proposed above.

Hopefully this helps. If it does, be sure to accept the solution so others in the community can find it. If not, please provide more context into your source data structures (tables, files, etc.) and your desired storage format in Fabric.