The determination of the specific angular momentum radial profile, $j(r)$, in the early stages of star formation is crucial to constrain star and circumstellar disk formation theories. The specific angular momentum is directly related to the largest Keplerian disk possible, and it could constrain the angular momentum removal mechanism. We determine $j(r)$ towards two Class 0 objects and a first hydrostatic core candidate in the Perseus cloud, which is consistent across all three sources and well fit with a single power-law relation between 800 and 10,000,au: $j_{fit}(r)=10^{-3.60pm0.15}left(r/textrm{1,000au}right)^{1.80pm0.04}$ km s$^{-1}$ pc. This power-law relation is in between solid body rotation ($propto r^2$) and pure turbulence ($propto r^{1.5}$). This strongly suggests that even at 1,000,au, the influence of the dense cores initial level of turbulence or the connection between core and the molecular cloud is still present. The specific angular momentum at 10,000,au is $approx3times$ higher than previously estimated, while at 1,000,au it is lower by $2times$. We do not find a region of conserved specific angular momentum, although it could still be present at a smaller radius. We estimate an upper limit to the largest Keplerian disk radius of 60,au, which is small but consistent with published upper limits. Finally, these results suggest that more realistic initial conditions for numerical simulations of disk formation are needed. Some possible solutions include: a) use a larger simulation box to include some level of driven turbulence or connection to the parental cloud, or b) incorporate the observed $j(r)$ to setup the dense core kinematics initial conditions.
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