Hi and welcome to the Forum.
In my .22/32 Kit Gun list I show 32230 shipping in February, 1958, and 31692 shipping in June, 1958. Neither of those are marked as Model 34. I would estimate yours to have shipped sometime in 1959, perhaps 1960. But since we don't know the rate at which these went out the door and S&W did not ship in serial order, that is only a guess. It could have been later.
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Jack
SWCA #2475, SWHF #318
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