We use 3 mm multiline and continuum CARMA observations toward the first hydrostatic core (FHSC) candidate L1451-mm to characterize the envelope kinematics at 1000 au scales and investigate its evolutionary state. We detect evidence of infall and rotation in the NH2D(11,1-10,1), N2H+(1-0), and HCN(1-0) molecular lines. We compare the position-velocity diagram of the NH2D(11,1-10,1) line with a simple kinematic model and find that it is consistent with an envelope that is both infalling and rotating while conserving angular momentum around a central mass of about 0.06 M o. The N2H+(1-0) LTE mass of the envelope along with the inferred infall velocity leads to a mass infall rate of approximately 6 ×10-6 M o yr-1, implying a young age of 104 years for this FHSC candidate. Assuming that the accretion onto the central object is the same as the infall rate, we obtain a minimum source size of 1.5-5 au, consistent with the size expected for a first core. We do not see any evidence of outflow motions or signs of outflow-envelope interaction at scales ≳2000 au. This is consistent with previous observations that revealed a very compact outflow (≲500 au). We conclude that L1451-mm is indeed at a very early stage of evolution, either a first core or an extremely young Class 0 protostar. Our results provide strong evidence that L1451-mm is the best candidate for being a bona fide first core.