basically you want to do a stream-stream join.  If you want to do that you need to take a few things into account (see link).
DLT might do this for you, but I never used it so I cannot confirm that.
If your source tables are delta tables, you could indeed use data feed.
Another option is to not use streaming and selecting the data from the source tables using a simple where condition.
Of course this will work but there is no management of state (what if a run has failed, what was the last update I did etc, unless you store some kind of watermark somewhere (without usign streams).