Flight Instructor reported a near miss with another aircraft while departing AVQ on a training flight. The reporter expressed concern that current procedures funnel traffic into dangerously close proximity.

Narrative

On a dual XC flight departing AVQ; we had a near miss while departing the area over the cement plant northbound. Local operations request all VFR traffic arrive and depart over the cement plant southeast of the field. Aircraft Y making no radio calls and not on our ADSB had overflown midfield for a teardrop entry for runway 12. They were at 4000' and we were at 3900' climbing to 6500' east of the field departing north. When I saw them in the left window; they were same altitude less than a quarter mile turning towards us fast. They were in our blind spot as we were climbing (they were slightly higher). I cut power and did an emergency descent to the right to avoid getting hit. That traffic also decided to turn and descend towards us at the same time while completing their teardrop. I estimated we were at the same altitude less than 100 feet away. Traffic never made any calls on the radio until after they had made their teardrop. They only popped up on ADSB as we were avoiding them and never got a traffic warning. That traffic started making calls after that and continued on another collision course with traffic already in the pattern. Standard practice from AVQ is to enter and exit the pattern over the cement plant to remain clear of housing. This practice however adds another layer of safety conflicts as more traffic is being funneled into one location. Increased operations with landings in-between taxiways midfield; prevent safe flights over the field. The other pilot's incorrect teardrop entry; 1000' above TPA (Traffic Pattern Altitude); over midfield; flying almost 3nm from the pattern; without making any radio calls was a major contributing factor. More awareness needs to be brought to AVQ for the heavy training and additional traffic that frequents the airport daily; and the nonstandard practices for the airport.