RV12 pilot on initial climb from a non-towered airport reported a NMAC with an air carrier which departed an intersecting runway.

Narrative

I departed ZZZ Runway XX in a RV-12iS on runway heading. I made standard call prior to taking Runway XX 'ZZZ Traffic; Light Sport Nxxxx taking Runway XX; northwest departure; ZZZ.' As I was climbing out; a narrow body twin engine jet of a Part 121 air carrier took Runway XY and departed on what would appear to be the ZZZ X Runway XY departure; in which they made an initial left turn on a west or southwest heading; before making a climbing right turn towards the east or southeast. I was approximately 3 nm north on runway heading when I made an in-air radio call: 'ZZZ Traffic; Light Sport Nxxxx; 3 nm northwest; northwest bound; climbing through 7500; ZZZ.' This call was made shortly after the jet departed Runway XY. Very soon I saw on ADS-B that the jet had turned left on a west or southwest heading; directly towards us. I was flying at 75 KIAS climbing at 600 FPM. I tried to make visual contact with the jet; but was unable. While looking for visual contact my ADS-B traffic on my Primary Flight Display (PFD) was showing the other traffic quickly approaching. ADS-B on my PFD had both visual and audio alerts regarding the proximity of the traffic. We (myself and passenger) did not see the jet until they had just crossed to the west of us; very close; and they were in a banked turn. This near miss occurred around 8200 ft. MSL 5NM northwest of ZZZ on the departure leg of Runway XX. I was preoccupied looking for visual contact and should have made an additional position reporting as the other aircraft approached. Time was moving slowly and too quickly at the same time. I don't know if the other aircraft heard my 3 nm northwest radio call. I don't know if they were still monitoring CTAF 122.8. I noted above that the part 121 jet appeared to be on the Runway XY ZZZX SID; and I suspect they had a RA because of the very close proximity. Next time I will try and make a radio call when I see aircraft on a converging course; definitely prior to close proximity. This incident also caught me by surprise by how quickly a fast moving aircraft (jet) can go from not being a factor to being a danger.