Didn't this happen already, or why else would nations like Argentina and Thailand have operated carriers until they ran out of money...?
Pre-WW2 can happen almost as in the OTL. Maybe have even more interest in circumventing the Washington Treaty by the major powers so that there are more hulls already in the beginning of the war in the major navies. Have Billy Mitchell taken seriously and not forced to resign?
Even without this, once it's clear that relations with the Soviets have turned sour (so already in 1945 before any of the WW2 carriers have been scrapped) have the US demand right from the start that its allies take a greater role in the anticipated Atlantic convoy escort and closing the GIUK gap - hence most NATO countries would operate at least one carrier to fill the commitment, initially surplus USN or RN hulls, later new designs lighter than a full supercarrier but still large enough to launch and recover a wider selection of jets than WW2 leftovers. In OTL, even the Netherlands had a light carrier so it's plausible to have a German carrier, Norwegian carrier, Greek carrier, etc. The Soviet Union counters this with the carriers of their own and imposes this requirement also to its satellites, so you would see actual Soviet carriers much earlier than OTL and have a Polish carrier, Bulgarian carrier, etc. China cannot be left behind the Soviet Union so also jumps in to the Carrier Race, prompting other Asian nations to follow suit. South Africa needs a carrier to support its Bush Wars, Pakistan will want to get even with India, etc.
With the advent of Harrier (and Yak-36/38) it becomes even easier and cheaper to operate a "carrier" since a through-deck cruiser is enough to act as a light carrier, even though for political reasons you would call it something else (as Japan is currently doing with its "helicopter-carrying destroyer" that conveniently can land F-35B's).
All this would make the current argument over Spratly and Paracel islands
much more interesting, with several carrier fleets playing chicken with the Chinese and each other...
