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Keep in mind something here. This isn't only nukes, but also the delivery system for them. So, that means you also need to have long range bombers by 1900 at least, or really massive artillery guns.
Regardless, your challenge is to advance science and technology enough for there to be nuclear bombs by the year 1900. In addition to that, no technology may be more primitive as a cost. So, things like medicine have to still be as far along as they were by 1900 at least, if not more from whatever POD you use.
Why? Well, I'm curious to see whether its possible make humanity advance technologically a lot faster. Additionally, such technological change would completely change how society functioned by such a date. Finally, we could use a TL that results in humanity having far more technological advance somehow.