No Korean War
The end of WW2 saw a huge cut in military budgets and a glut of WW2 surplus. WW2 jets were expensive and loaded with flaws, while even better piston aircraft coming off the production lines. Without a major war, militaries could return to their relatively slow 5-10 year development cycle, not the hectic 1-3 years of WW2.
Then North Korea (backed by the Soviet Union) invaded South Korea (backed by the UN), and the world entered the Cold War; an era of constant war-like military budgets. Money poured back into military procurement, and new designs poured off the production lines.
But if the Korean War didn't happen, the major powers wouldn't be at each other's throats, and there would be less pressure to technologically one-up each other. Smaller conflicts could be handled with existing stockpiles. The whole Western Pacific might have avoided decades of destabilizing foreign imposed ideological divisions and proxy wars. Militaries and their budgets would have remained more complacent delaying the domination of jets.
WW2 Jets Were Expensive Prototypes
The first generation jets of WWII had many problems yet to be solved before they could become truly superior to piston aircraft. These were more prototypes than production aircraft. They were hurriedly designed, fuel hungry, low endurance, maintenance intensive, and expensive. Jets began to push into the transonic, a poorly understood area of aeronautics where some of the air flowing over the aircraft goes supersonic and some is subsonic, and the straight-winged designs of the 1940s could not cope.
For example, the US P-80 Shooting Star and the Soviet MiG-9.
The end of the war also saw piston fighter aircraft reach their pinnacle with record-breaking aircraft such as the Twin Mustang, the F8F Bearcat, and the Soviet La-9.
Who's going to pay for it?
A few years after the war saw refined designs with reliable engines, acceptable endurance, and swept-wings to solve the problems of transonic flight. For example, the US F-86 Sabre and Soviet MiG-15.
These were both operational in 1949/50 and dominated the skies... once there were enough of them, but who's going to pay for it?
After WWII, the Western Allies wanted to get on with rebuilding and generally returning to life as normal. They found themselves with a huge military surplus and no major threats... except their nominal allies the USSR. Production orders were slashed. Experimental projects were ended. Post-war armies would largely be made up of WWII surplus, with low production numbers of promising designs. Why build expensive jet aircraft when you had huge stockpiles of piston aircraft which worked just fine? That was the plan.
War Were Declared
The Western Allies were in the process of demobilizing when war were declared. North Korea had invaded South Korea, and the UN was going to stop them.
Initially the war was fought with surplus WWII equipment, but production lines quickly ramped up and the new post-war jets appeared in large numbers to dominate the skies...
...but only high-performance fighters. The rest of the air fleets were still piston-engined: bombers, attack aircraft, transports, etc. They got the job done; in many cases jets of the time were not capable of performing their missions requiring high endurance and many frequent sorties, and would not be for decades. The low numbers and many drawbacks of the jet fighters of the time meant even piston-engined fighters remained in front-line service.
What if Korea united as intended?
WW2 ended with formerly Japanese-occupied Korea now occupied by the Soviets in the north and the US in the south. The Soviets and US agreed in principle to withdrawing, but required a five year "trusteeship" of divided military occupation, much like Germany. And much like Germany, the divergent political philosophies and mistrust between the powers created a divide which previously hadn't existed.
What if the foreign militaries withdrew and allowed Korea to form a government peacefully? The Koreans hated the trusteeship; after decades of Japanese rule they were ready to get on with self-government. With an independent Korea a major (proxy) war between the US, Soviets, and China would be averted and the occupying armies could withdraw.
A more stable Western Pacific?
A stable Korea means no US troops in mainland Asia to inflame the Soviets and Chinese. The Soviets and Chinese no longer had to worry about a US army on their doorstep, and the US would feel less need to keep military forces in Japan. Without the Korean War to inflame US-Chinese relations, the US may not have felt compelled to get involved in the Chinese Civil War allowing that conflict to definitively end.
Your world could see a more stable Western Pacific. Without US and Soviet blood being spilled in the Korean War, the wars of decolonization against the Western Powers would not be seen as an ideological struggle against Soviet Communism, the US would be less compelled to intervene on behalf of the British, Dutch, and French, and the region could sort itself out. For example, with no US assistance, Vietnam could have gained its independence after defeating their French overlords in 1954 avoiding decades of proxy warfare in the region. With the conflict no longer being seen as a proxy war, no destabilizing partition of Vietnam would be necessary.
You don't need expensive jets for brush wars.
Without the major powers in active conflict, there would be less pressure for an arms race. Smaller countries and rebellions would not have the resources to compete technologically and could be handled with existing stockpiles and low production runs. Without the pressure of combat against a peer adversary, designs would evolve slower and with more missteps. Better jets would come, but slower, fewer in number, and less refined.