Pebble accretion is a new mechanism to quickly grow the cores of planets. In pebble accretion, gravity and gas drag conspire to yield large collisional cross sections for small particles in protoplanetary disks. However, before pebble accretion commences, aerodynamical deflection may act to prevent planetesimals from becoming large, because particles tend to follow gas streamlines. We derive the planetesimal radius where pebble accretion is initiated and determine the growth timescales of planetesimals by sweepup of small particles. We obtain the collision efficiency factor as the ratio of the numerically-obtained collisional cross section to the planetesimal surface area, from which we obtain the growth timescales. Integrations are conducted in the potential flow limit (steady, inviscid) and in the Stokes flow regime (steady, viscid). Only particles of stopping time $t_s ll t_X$ where $t_Xapprox10^3$ s experience aerodynamic deflection. Even in that case, the planetesimals gravity always ensures positive collision factors. The maximum growth timescale occurs typically at around $Rapprox100 mathrm{km}$, but is less for colder disks, corresponding to interactions shifting to the Safronov focusing regime. For particles $t_s gg t_X$ pebble accretion commences only after this phase and is characterized by a steep drop in growth timescales. Consequently, at distances beyond ~10 AU sweepup growth timescales are always longer than $10$ Myr, while in the inner disk (~<3 AU) the viability of the sweepup scenario is determined by the outcome of pebble-planetesimal collisions in the geometric regime. We present analytical fits for the collision efficiency factors and the minimum planetesimal size needed for pebble accretion. (Abridged)
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