A Center Controller reported after they took over a busy combined sector they failed to notice an air carrier conflicting with an unidentified VFR target.

Narrative

The sector I had been working when I originally came in today; closed (Sector XX) and I was running the list to get the next person out; which was the controller at Sector Y (combined with Sector Z). As I was previewing the sector; I saw the EDST (En Route Decision Support Tool) had over half a page of aircraft and a lot of military airspace was active on the scope. During the position relief briefing; the controller stated there was an aircraft cleared out of ZZZ and we were waiting for them to depart (Aircraft X). There was also another GA arrival going into ZZZ1 (another uncontrolled airport); who had all the information and was looking for a visual. At the time; there were multiple VFR aircraft on codes for flight following; many VFR targets throughout; and a steady amount of traffic (both IFR and VFR) transitioning through the combined sectors. Aircraft X had initially checked in after departing; climbing to 3000 per the original clearance. As I was sitting down at the scope; I went to call and coordinate a point-out and cancel the block with ZZZ2; but saw a VFR traffic in front of Aircraft X; which I immediately hung up the line and called traffic. The VFR target was at their 1 o'clock and moving slightly northeast bound when I called it with Aircraft X climbing about a mile south of the target. I did not have full altitude visible since the Airline's datablock had partially obscured it. To the best of my ability; I saw 2000 + then on the next hit saw 3000 on the VFR target. Aircraft X said they had traffic in sight and the traffic was 500ft above them. Aircraft X then said they would respond to the RA and descended back down to 2000 until clear. Before the relieved controller left the area; I had them sit back down on the D-side until I could regain control of the sector. There were many aircraft coming in and out of the sector with multiple departures from all of the adjacent approach controls and military aircraft with requests.Spend more time previewing and having a better handle of a busy sector before taking it. Making sure there are no immediate potential conflicts at those sectors or addressing those conflicts with the controller being relieved before assuming the position.