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 f it (r) = 10 −3.60±0.15 (r/1,000 au) 1.80±0.04 km s −1 pc. This power-law relation is in between solid body rotation (∝ r 2 ) and pure turbulence (∝ r 1.5 ). This strongly suggests that even at 1,000 au, the influence of the dense core's 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 ≈ 3× higher than previously estimated, while at 1,000 au it is lower by 2×. 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.