The problem that you are describing could be
cold start injector time switch related
Fig. 1: Cutaway view of the cold start injector
During cold engine starting, the cold start injector is used to supply additional fuel to the intake manifold to aid in initial start-up. The opening and closing of the injector is determined by the Start Injector Time Switch. when the engine coolant temperature falls below a certain point, the switch opens cold start injector.

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