Newborn pulsars resulting from core-collapse supernovae are promising sources of high-energy (HE) cosmic rays and neutrinos. In this work, we focus on HE neutrinos generated through interactions between protons accelerated in relativistic pulsar winds and the supernova (SN) ejecta. Using a binned likelihood analysis, we evaluate the detection prospects of these neutrinos with IceCube and explore their potential for probing the initial spin period ($P$) and magnetic field strength ($B$) of newborn pulsars. Noticing a degeneracy in neutrino signal with $B/P^2$ across a broad parameter space, we find that HE neutrinos from a Galactic newborn pulsar ($d=10\mathrm{kpc}$) with $(B/{10}^{12}\mathrm{G})(P/\mathrm{ms}{)}^{-2}\gtrsim 0.003$ can be detected at $\gtrsim 3\sigma$ significance. Even in the absence of a nearby pulsar, the diffuse flux from the cosmologic population of pulsars could be probed by next-generation detectors like IceCube-Gen2 and Giant Radio Array for Neutrino Detection 200k. For Galactic pulsars with $(B/{10}^{12}\mathrm{G})(P/\mathrm{ms}{)}^{-2}\gtrsim 0.08$, the combination $B/P^2$ can be measured with an accuracy of better than 20% at the $3\sigma$ confidence level. Additionally, we show that for pulsars with detectable HE neutrino signals, the emission can be clearly distinguished from neutrinos produced by interactions between SN ejecta and the circumstellar medium, due to their distinct temporal and spectral features.

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