How did academics support hypotheses before the null hypothesis significance testing (NHST) framework was, in part, introduced and democratized by Fisher/Neyman & Pearson? Suppose NHST was never a thing, what are some plausible frameworks academics could employ to support their hypotheses today? Are there alternatives based on mathematics outside of statistics and/or probability?
Neither Fisher nor Neyman and Pearson proposed a "null hypothesis significance testing framework". Instead, Fisher demonstrated the significance testing framework and Neyman and Pearson later demonstrated the hypothesis testing framework. They are not the same and they are not similar in their objectives. The significance testing framework attempts to quantify the evidence in the data against a null hypothesis, and uses a continuous p-value. The hypothesis testing procedure entails a decision to reject or not reject the null hypothesis and it does not use a p-value.
The NHST hybrid that you ask about is an incoherent mixture of two incompatible approaches. Neither Fisher nor Neyman and Pearson would be happy to have their names attached.
Please see this paper for a more complete explanation: https://link.springer.com/chapter/10.1007/164_2019_286